Перев. с англ. под ред. В.А. Артамонова. — М.: Физматлит, 2004. — 350 c. — ISBN 5-9221-0400-4. Книга написана выдающимся американским математиком С. Маклейном, одним из создателей теории категорий, рассматривающей свойства отображений (морфизмов) между объектами с определённой структурой. Овладение категорным языком и умение его использовать позволяет современному математику...
М.: Мир, 1972. — 259 с. Книга румынских математиков представляет собой введение в теорию категорий, методы и язык которой применяются почти во всей современной математике. Приводятся многочисленные примеры ситуаций из различных разделов математики, которые иллюстрируют универсальность рассматриваемых понятий. Книга может служить учебным пособием для изучающих современную...
Перев. с англ. под ред. В.А. Артамонова. — М.: Физматлит, 2004. — 350 c. — ISBN 5-9221-0400-4. Книга написана выдающимся американским математиком С. Маклейном, одним из создателей теории категорий, рассматривающей свойства отображений (морфизмов) между объектами с определённой структурой. Овладение категорным языком и умение его использовать позволяет современному математику...
2nd Ed. — NY.: Oxford University Press (1st published 2006), 2010. — (xvi+311) p. (Oxford Logic Guides. 52 ). — ISBN: 978–0–19–923718–0 (Pbk.), English. Interactive menu. Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science,...
Boston: MIT Press, 2014. — 486 p. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent...
Учебно-методическое пособие. — Саратов: Саратовский государственный университет имени Н.Г. Чернышевского (СГУ), 2003. — 63 с. Язык теории категорий используется во многих областях современной математики. Данное пособие имеет цель научить основам языка теории категорий и на примерах продемонстрировать категорную природу таких хорошо известных конструкций, как тензорное...
Учебное пособие. — Palmarium Academic Publishing, 2013. — 80 с. — ISBN 9783659985355. Теория категорий в России не входит в учебные программы университетов и в то же время является фундаментальной и необходимой частью математического образования. Она имеет непосредственное применение в математике, физике, логике и компьютерных науках. Учебное пособие рассчитано на первое...
М.: Наука, Главная редакция физико-математической литературы, 1974. — 256 с. — (Современная алгебра). Характерной чертой современной математики является изучение математических объектов вместе с отображениями этих объектов друг в друга, согласованными со структурой объектов: теория множеств немыслима без отображений множеств, топология немыслима без непрерывных отображений,...
Учебное пособие. — Саратов: Наука, 2012. — 86 с. — ISBN: 978-5-9999-1223-7. Первая часть пособия по теории категорий для студентов-математиков. Данное издание представляет собой пособие по теории категорий для студентов механико-математического факультета. Оно охватывает темы: определение и примеры категорий, сумма и произведение в категории, универсальные объекты, дуальная...
Москва: Московский государственный университет имени М.В. Ломоносова (МГУ), 1970. — 280 с. Характерной чертой современной математики является изучение математических объектов, вместе с отображениями этих объектов друг в друга, согласованными со структурой объектов. Обычно объекты и их отображения образуют категорию. Именно поэтому теоретико-категорный язык с момента своего...
UK.: Cambridge University Press, 1997. - 358 p. - ISBN: 0-521-47249-0, eBook, English In the last fifty years, the use of the notion of 'category' has led to a remarkable unification and simplification of mathematics. Written by two of the best-known participants in this development, Conceptual mathematics is the first book to apply categories to the most elementary...
Cambridge University Press, Cambridge , 2011, 236p.,
Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning...
Springer International Publishing AG, CH, 2017. — 174 p. — (Compact Textbooks in Mathematics) — ISBN: 9783319419169 The purpose of this little book is to provide an introduction to the basic concepts of category theory. It is intended for the graduate student, advanced undergraduate student, nonspecialist mathematician or scientist working in a need-to-know area. The treatment...
М.: Мир, 1972. — 259 с. Книга румынских математиков представляет собой введение в теорию категорий, методы и язык которой применяются почти во всей современной математике. Приводятся многочисленные примеры ситуаций из различных разделов математики, которые иллюстрируют универсальность рассматриваемых понятий. Книга может служить учебным пособием для изучающих современную...
Учебное пособие. — Саратов: Наука, 2012. — 92 с. Вторая часть. Данное издание представляет собой пособие по теории категорий для студентов механико-математического факультета. Оно охватывает темы: функторные морфизмы (естественные преобразования), эквивалентность категорий, представимые функторы, пределы и копределы, группы в категориях, сопряженные функторы. Каждое вводимое...
Учебное пособие. — Луганск: Луганский государственный педагогический университет имени Тараса Шевченко (ЛГПУ), 2004. — 60 с. Введение. Определение и примеры категорий. Типы морфизмов и объектов. Конструкции категорий. Функторы. Пределы. Копределы. Естественные преобразования. Сопряженные функторы. Приложение. Категорийные в нуле полугруппы. Литература. Предметный указатель.
Canada.: TAC, 2012 (No. 22), — 538 p., eBook, English. ( Free Published ). [Reprints in Theory and Applications of Categories ( TAC ), No. 22, 2012] Transmitted by Richard Blute, Robert Rosebrugh and Alex Simpson. Reprint published on 2012-09- 19. Canada, Free Publications]. [Reprint with Correction, Original Published: 3rd Ed. (1st publ. 1990; 2nd, 1995). - UK.: Prentice Hall,...
Ver. 1.3. — GitHub, 2019. — 498 p. I will attempt, in the space of a few paragraphs, to convince you that this book is written for you, and whatever objections you might have to learning one of the most abstract branches of mathematics in your “copious spare time” are totally unfounded. My optimism is based on several observations. First, category theory is a treasure trove of...
М.: Национальный исследовательский университет "Высшая школа экономики" (НИУ ВШЭ), 2018. — 137 с. Вводный курс гомологической алгебры для студентов 2-3 курса бакалавриата и 1 курса магистратуры, ориентированный на тех, кто собирается изучать алгебраическую геометрию и геометрическую теорию представлений. Пререквизиты: первые 3 семестра стандартных начальных курсов алгебры,...
Second Edition. — N.Y.: Springer, 1971. — 314 p. (1st published 1998). — ISBN: 0-387-98403-8, eBook, Interactive menu. English. Preface to the Second Edition. This second edition of "Categories Work" adds two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them-items of interest in...
MIT Press, 1991, 100 p.
Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists...
Cambridge University Press, 2019. — 352 p. — ISBN: 978-1-108-48229-5. Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication...
Oxford: Oxford University Press, 2018. — 528 p. Often people have wondered why there is no introductory text on category theory aimed at philosophers working in related areas. The answer is simple: what makes categories interesting and significant is their specific use for specific purposes. These uses and purposes, however, vary over many areas, both "pure", e.g., mathematical,...
Cambridge University Press, 2022. — 438 p. — ISBN 9781108769389. Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no...
New York: Dover Publications, 2016. — 258 p. — (Aurora: Dover Modern Math Originals). — ISBN: 048680903X. Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester introduction to the subject is derived from courses that author Emily Riehl taught at Harvard and Johns...
Без выходных данных. Файл для адептов теории категорий. Представляет собой заготовку для распечатки игральных карт, на каждой из которых приводится аксиома, теорема или какое-либо свойство из теории категорий. Файл подготовлен анонимным любителем теории категорий.
М.: Наука, Главная редакция физико-математической литературы, 1974. — 256 с. — (Современная алгебра). Характерной чертой современной математики является изучение математических объектов вместе с отображениями этих объектов друг в друга, согласованными со структурой объектов: теория множеств немыслима без отображений множеств, топология немыслима без непрерывных отображений,...
Cambridge University Press, UK, 2014. — 192 p. — (Cambridge Studies in Advanced Mathematics 143) — ISBN10: 1107044243. At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal...
The MIT Press, 1991. — 295 p.
Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the...
Mount Allison: TAC, 2006 (no. 17), — 509 p. eBook, Interactive menu. English. ( Free Published ). Reprints in: Theory and Applications of Categories ( TAC ) No. 17, 2006. Originally published as: Abstract and Concrete Categories, John Wiley and Sons, 1990. Sciences have a natural tendency toward diversification and specialization. In particular, contemporary mathematics...
ArXiv, 2018. — 62 с. Теория категорий в России не входит в учебные программы университетов и в тоже время является фундаментальной и необходимой частью математического образования. Учебное пособие рассчитано на первое ознакомление с теорией категорий широкого круга читателей : школьников, студентов, научных работников разных специальностей. Категории и функторы Определение...
Blurb.com, 2018. — 492 p. I will attempt, in the space of a few paragraphs, to convince you that this book is written for you, and whatever objections you might have to learning one of the most abstract branches of mathematics in your “copious spare time” are totally unfounded. My optimism is based on several observations. First, category theory is a treasure trove of extremely...
Перевод и редактирование Г. Чернышёва. — 461 с. Излагаются основы теории категорий с точки зрения программирования, прежде всего, на языках функционального типа. Доказательства категорных свойств, как правило, не приводятся, но объясняются программными конструкциями. Такая возможность позволяет осветить значительный объем сведений по теории категорий, имеющих полезные...
Фоккинга М. Мягкое введение в теорию категорий. Впервые опубликовано в 1992 г. (университет Утрехта). Данный файл представляет собой версию от 1994 г., улучшенную автором. Краткое содержание: The main concepts. a Categories. b Functors. c Naturality. d Adjunctions. e Duality. Constructions in categories. a Iso, epic, and monic. b Initiality and nality. c Products and Sums. d...
Springer, 2019. — 139 p. — (Springer Proceedings in Physics 235). — ISBN: 978-3-030-30895-7. The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches...
Cambridge University Press, 2014 — 352 pp — (New Mathematical Monographs: 24). This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit...
Cambridge University Press, 1997. — 374 p. — ISBN 0-521-47249-0. The idea of a "category" - a sort of mathematical universe - has brought about a remarkable unification and simplification of mathematics. Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two...
Cambridge University Press, 2011 — 652 pp. — (New Mathematical Monographs: 19). The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of...
Cambridge University Press, 1994. — 358 p. A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. After introducing the terminology and proving the...
Springer-Verlag Berlin Heidelberg, 2006. — 495 p. The language of Mathematics has changed drastically since the middle of the twentieth century, in particular after Grothendieck’s ideas spread from algebraic geometry to many other subjects. As an enrichment for the notions of sets and functions, categories and sheaves are new tools which appear almost everywhere nowadays,...
Bartosz Milewski, 2017. — 510 p. Category: The Essence of Composition Types and Functions Categories Great and Small Kleisli Categories Products and Coproducts Simple Algebraic Data Types Functors Functoriality Function Types Natural Transformations Declarative Programming Limits and Colimits Free Monoids Representable Functors The Yoneda Lemma Yoneda Embedding It’s All About...
Prentice Hall, 1988. — 263 p.
Why should there be a book with such a strange title as this one? Isn't category theory supposed to be a subject in which mathematical structures are analyzed on such a high level of generality that computations are neither desirable nor possible? Historically, category theory arose in algebraic topology as a way to explain in what sense the passages...
Massachusetts Institute of Technology, 2013. — 263 p. An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields...
Cambridge University Press, 1994. — 534 p. The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important...
Перевод и редактирование Г. Чернышёва. — 149 с. Изложены базовые понятия теории категории, важные для использования в языках программирования. Наглядность изложения материала обеспечивается графической демонстрацией с использованием струнных диаграмм. Приводятся основы лямбда-исчисления.
Cambridge University Press, 1994. — 456 p. The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important...
Scala ed. — GitHub, 2018. — 582 p. This is the Scala edition of Category Theory for Programmers . It’s been a tremendous success, making Bartosz Milewski’s seminal work available as a nicely typeset PDF, as well as a hardcover book. There have been numerous contributions made to improve the book, by fixing typos and errors, as well as translating the code snippets into other...
Singapore: World Scientific, 2018. — 152 p. Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a deeper understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a...
Springer International Publishing AG, 2017. — 113 p. — (Compact Textbooks inMathematics) — ISBN: 3319572180. This book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word. The focus lie on the relationships which a group may have with other groups, via “universal properties”, a view on that...
Cambridge University Press, 2019. — 450 p. — (Cambridge Studies in Advanced Mathematics: 180). — ISBN: 978-1-108-47320-0. This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to methods used at the forefront of research in algebraic topology and algebraic geometry in the twenty-first century. The...
Berlin: Helderman Verlag, 2007. — 409 p. Our in purpose in writing this book is to present the theory of categories at earliest moment at which the reader can appreciate it, that is, as soon he becomes reasonably acquanted with set theory, modern algebra, and general topology. It is hoped that such a presentation will help him to prepare for advanced topics om these subjects and...
London: Academic Press, 1973. — 480 p. — ISBN: 0125615507, 9780125615501
The theory of abelian categories begins almost with the first studies on abelian groups. A first systematization of the notions and results is made by Cartan and Eilenberg for categories of modules and subsequently generalized by Buchsbaum through the introduction of the notion of exact category.
An...
Online ed. - Montreal: Université de Montréal, 2020. - 567 p. This book is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. We expound the constructions we feel are basic to category theory in the context of examples and applications to computing science . Some categorical ideas and constructions are already...
Tokyo.: John Weatherhill, Inc., 1984 (1st printing, Sept. 1966). — 164 p. English. ( OCR-Слой ). If topology were publicly defined as the study of families of sets closed under finite intersection and infinite unions a serious disservice would be perpetrated on embryonic students of topology. The mathematical correctness of such a definition reveals nothing about topology...
Oxford University Press, 2020. — 337 p. — (Oxford Graduate Texts in Mathematics 28). — ISBN-13 9780198739623. Categories for Quantum Theory: An Introduction lays foundations for an approach to quantum theory that uses category theory, a branch of pure mathematics. Prior knowledge of quantum information theory or category theory helps, but is not assumed, and basic linear...
Springer, 1998. — 326 p. — ISBN-10 1441931236. An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets...
De Gruyter, 2023. — 436 p. — ISBN 978-3-11-108056-7. This book presents the formal definition of fundamental transformations in Category Theory as a mathematical language to be used in Computer Science modelling. The book focuses in particular on models with Global and Internal symmetries (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second...
Singapore: World Scientific Publishing Company, 2024. — 463 p. — ISBN 9811286000. One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and...
Cambridge University Press, 2020. — x, 390 p. — (Cambridge Studies in Advanced Mathematics, 188). — ISBN: 978-1-108-47962-2. True PDF Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the...
Перевод и редактирование Г. Чернышёва. — 461 с. Эта книга — приглашение открыть для себя передовые темы теории категорий на конкретных примерах из реальной жизни. Она содержит доступное, быстрое введение, подготавливающее более успешное усвоение дальнейшего материала. Темы книги касаются семи областей, каждая из которых сочетает вызывающие воспоминания приложения, такие как...
Москва: Московский государственный университет имени М.В. Ломоносова (МГУ), 1970. — 280 с. Характерной чертой современной математики является изучение математических объектов, вместе с отображениями этих объектов друг в друга, согласованными со структурой объектов. Обычно объекты и их отображения образуют категорию. Именно поэтому теоретико-категорный язык с момента своего...
Cambridge: Cambridge University Press, 2023. — 197 p. String diagrams are powerful graphical methods for reasoning in elementary category theory. Written in an informal expository style, this book provides a self-contained introduction to these diagrammatic techniques, ideal for graduate students and researchers. Much of the book is devoted to worked examples highlighting how...
Springer-Verlag, 1967. — 164 p. — (Lecture Notes in Mathematics). A collection of informal reports and seminars Edited by A. Dold, Heidelberg and B. Eckmann, Zurich Daniel G. Quillen. Massachusetts Institute of Technology Cambridge, Mass. Homotopical Algebra or nonlinear homological algebra is the generalization of homological algebra to arbitrary categories which results by...
Manchester: Manchester University, 2005. - 197 p.
Notes for a course offered as part of the MSc. in Mathematical Logic, Manchester University. From the table of contents: Development and exercises; Functors and natural transformations; Limits and colimits, a universal solution; Cartesian closed categories.
Перевод и редактирование Г. Чернышёва. — 499 с. Данная книга содержит изложение теоретических и прикладных основ функционального программирования, базирующихся на понятиях теории категорий. Назначение книги (как и предыдущей книги автора, «Теория категорий для программистов», множества его публикаций и видео-трансляций) — подготовить заинтересованного читателя к более глубокому...
Oxford: Oxford University Press, 2021. — 613 p. — ISBN 0198871376. Category theory emerged in the 1940s in the work of Samuel Eilenberg and Saunders Mac Lane. It describes relationships between mathematical structures. Outside of pure mathematics, category theory is an important tool in physics, computer science, linguistics, and a quickly-growing list of other sciences . This...
River Edge: North Holland, 1990. — 315 p. General concepts and methods that occur throughout mathematics – and now also in theoretical computer science – are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric nature of the subject and explaining its connections to mathematical logic. The book should appeal to the inquisitive reader who...
Birkhauser, 2021. — 300 p. — (Compact Textbooks in Mathematics). — ISBN 978-3030615239. This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics. It treats the basics of the theory and supplies all the necessary details while leading the reader along a streamlined path from the basic definitions to more...
Ver. 1.3. — GitHub, 2019. — 498 p. — ISBN: n/a. Code files only! Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained...
Springer, 2019. — 343 p. — (Algebra and Applications 26). — ISBN: 978-3-030-05673-5. This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict n-categories are easily defined in...
New York: Dover Publications, 2016. — 258 p. — (Aurora: Dover Modern Math Originals). — ISBN: 048680903X. Corrected online edition ! A number of small typos and the mathematicial errors mentioned below have been corrected in the online version of the book. The page numbers refer to the published version of the text. См.: /file/2240821/
Учебное пособие. — Перевод и редактирование Г. Чернышёва. — 66 с. Эти заметки, разработанные в течение шести лет, были написаны для курса из восемнадцати лекций по теории категорий. Хотя в значительной степени они основаны на категориях МакЛейна для работающих математиков, курс был разработан, чтобы быть самодостаточным, с демонстрацией большинства примеров из самой теории...
New York: Springer, 2021. — 326 p. Highlights the key points of the theory before discussing various properties and structures that a model category may have Boasts over 200 pages of examples of model categories in algebra and topology, and everything in between, ranging over 12 themes Features a table of curiosities highlighting a range of, sometimes unexpected, phenomena that...
Cambridge: Cambridge University Press, 2019. — 330 p. — (Cambridge Tracts in Mathematics 215). —ISBN: 978-1-108-47442-9. Slenderness is a concept relevant to the fields of algebra, set theory, and topology. This first book on the subject is systematically presented and largely self-contained, making it ideal for researchers and graduate students. The appendix gives an...
Cambridge University Press, 2020. — 622 p. — (Cambridge Studies in Advanced Mathematics, 183). — ISBN: 978-1-108-41933-8. There have been remarkably few systematic expositions of the theory of derived categories since its inception in the work of Grothendieck and Verdier in the 1960s. This book is the first in-depth treatment of this important component of homological algebra....
Перев. с англ. Д.А. Райкова и В.С. Ретиха. — С примечанием Д.А. Райкова. — Москва: Мир, 1972. — 257 с. Книга румынских математиков представляет собой введение в теорию категорий, методы и язык которой применяются почти во всей современной математике. Приводятся многочисленные примеры ситуаций из различных разделов математики, которые иллюстрируют универсальность рассматриваемых...
Singapore: World Scientific Publishing Company, 2020. — 535 p. The study of higher dimensional categories has mostly been developed in the globular form of 2-categories, n-categories, omega-categories and their weak versions. Here we study a different form: double categories, n-tuple categories and multiple categories, with their weak and lax versions.We want to show the...
Cambridge: Cambridge University Press, 2013. — 288 p. Higher category theory is an increasingly important discipline with applications in topology, geometry, logic and theoretical computer science. This comprehensive treatment covers essential material for any student of coherence, or for any researcher wishing to apply higher categories or coherence results in fields such as...
Springer-Verlag Berlin Heidelberg, 2008. — 340 p. — (Lecture Notes in Physics 726). — ISBN: 978-3-540-74956-1 (eBook), 978-3-642-09436-1 (Softcover), 978-3-540-74955-4 (Hardcover). Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in...
Springer-Verlag, London, Limited, 2012. — 307 p. — (Algebra and Applications 17) — ISBN: 1447122933. The most important invariant o a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far...
Cambridge: Cambridge University Press, 2004. — 448 p. Category theory has experienced a resurgence in popularity recently because of new links with topology and mathematical physics. This book provides a clearly written account of higher order category theory and presents operads and multicategories as a natural language for its study. Tom Leinster has included necessary...
Cambridge University Press, 2020. — 597 p. — (Cambridge Studies in Advanced Mathematics 189). — ISBN: 9781108867351. Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the...
UK.: Prentice Hall, 1990. — 448 p. — ISBN: 0-13-120486-6, English. ( OCR-Слой ). This book is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. We expound the constructions we feel are basic to category theory in the context of examples and applications to computing science. Some categorical ideas and...
Singapore: World Scientific, 2020. — 214 p. The aim of the book is to present a precise and comprehensive introduction to the basic theory of derived functors, with an emphasis on sheaf cohomology and spectral sequences. It keeps the treatment as simple as possible, aiming at the same time to provide a number of examples, mainly from sheaf theory, and also from algebra. The...
Springer, 2024. — 1130 p. Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck’s Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand. This book guides readers familiar with rings and modules through the...
Cambridge University Press, 2022. — 781 p. — (Cambridge Studies in Advanced Mathematics 194). — ISBN-13 9781108837989. The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question...
Springer, 2020. — 250 p. — (Lecture Notes in Mathematics 2279). — ISBN 978-3-030-61202-3. This monograph introduces involutive categories and involutive operads, featuring applications to the GNS construction and algebraic quantum field theory. The author adopts an accessible approach for readers seeking an overview of involutive category theory, from the basics to cutting-edge...
Berlin, Germany: European Mathematical Society, 2020. — 475 p. — (EMS Series of Congress Reports). — ISBN: 978-3-03719-198-9. This volume contains research and survey articles on Drinfeld modules, Anderson t-modules and t-motives. Much material that had not been easily accessible in the literature is presented here, for example the cohomology theories and Pink’s theory of Hodge...
Springer, 2014. — 486 p. — (Contributions in Mathematical and Computational Sciences 7). — ISBN: 9783642552441. One can argue that Iwasawa Theory has its roots in the early nineteenth century and in the work of Ernst Kummer (29 January 1810–14 May 1893), who studied the class number of the cyclotomic field Q. p/, in his approach to prove Fermat’s Last Theorem. Kummer not only...
Cambridge University Press, 2025. — 439 p. Offering a unique resource for advanced graduate students and researchers, this book treats the fundamentals of Quillen model structures on abelian and exact categories. Building the subject from the ground up using cotorsion pairs, it develops the special properties enjoyed by the homotopy category of such abelian model structures. A...
Paris: Société mathématique de France, 2017, — 134 p. Voevodsky defines a triangulated category /K(k) and shows that this category possesses many of the properties that the derived category of a conjectural category of mixed motives would satisfy. One unsatisfactory aspect of his theory was that most of the results about non-smooth varieties, for example that higher Chow groups...
Birkhäuser, 2024. — 300 p. — (Computer Science Foundations and Applied Logic). — ISBN 3031685377. This unique book offers an introductory course on category theory, which became a working language in algebraic geometry and number theory in the 1950s and began to spread to logic and computer science soon after it was created. Offering excellent use of helpful examples in Haskell...
Springer, 2022. — 159 p. — ISBN 978-3-031-14208-6. Классически полупростые кольца: взгляд через модули и категории Classically Semisimple Rings is a textbook on rings, modules and categories, aimed at advanced undergraduate and beginning graduate students. This book is written for advanced undergraduate and beginning graduate students. It tells the story of a classical...
Paris: Sorbonne Universite, 2023. — 219 p. This text may be considered as an elementary introduction to the book [Categories and Sheaves - Masaki Kashiwara, Pierre Schapira] and in fact a few (as few as possible) difficult proofs, such as the Brown representability theorem, are omitted here, with the reader referred to that book. On the other hand, we study in some details...
Massachusetts Institute of Technology, 2013. — 263 p. An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields...
Cambridge, Massachusetts: MIT Press, 1991. — 328 p. — (Foundations of Computing Series). — ISBN 0262011255. Category theory has become a fundamental tool in theoretical computer science, and especially for the meta-theory of programming languages. This book provides a self-contained introduction to the subject, especially meant for students in computer science. The main...
Oxford: Clarendon Press, 1992. — 283 p. Zariski categories Classical objects Spectra Schemes Jacobson ultraschemes Algebraic varieties Zariski toposes Neat objects and morphisms Flatness properties Etale objects and morphisms Terminators Some constructions of Zariski categories Index of symbols Index of terms
Springer, 2019. — 230 p. — (Lecture Notes in Mathematics 2244). — ISBN: 978-3-030-27122-0. This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional...
New York: Springer, 2015. — 358 p. The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads and enable one to encode bialgebraic, rather than just (co)algebraic, structures. The text extends both the Joyal-Lurie approach to higher categories and...
American Mathematical Society, 2002. — 349 p. — (Mathematical Surveys and Monographs Volume 96). Introduction and History. Operads in a Symmetric Monoidal Category. Topology - Review of Classical Results. Algebra. Geometry. Generalization of Operads.
Princeton: Princeton University Press, 2001. — 451 p. The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new...
Cambridge: Cambridge University Press, 2003. — 433 p. Researchers, teachers and graduate students in algebra and topology--familiar with the very basic notions of category theory--will welcome this categorical introduction to some of the key areas of modern mathematics, without being forced to study category theory. Rather, each of the eight largely independent chapters...
World Scientific Publishing, 2022. — 486 p. — ISBN 9811250928. Бесконечные операды и моноидальные категории с групповой эквивариантностью This monograph provides a coherent development of operads, infinity operads, and monoidal categories, equipped with equivariant structures encoded by an action operad. A group operad is a planar operad with an action operad equivariant...
Springer, 2019. — xv, 218 p. — (Lecture Notes in Mathematics, 2244). — ISBN: 978-3-030-27122-0, 978-3-030-27124-4. True PDF This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to...
Springer, 1966. — xviii + 562 p. — ISBN13: 978-3-642-99904-8. This volume contains the articles contributed to the Conference on Categorical Algebra, held June 7—12, 1965, at the San Diego campus of the University of California under the sponsorship of the United States Air Force Office of Scientific Research. Of the thirty-seven mathematicians, who were present seventeen...
Berlin: Springer-Verlag, 1969. — 222 p. — (Lecture Notes in Mathematics 86). M. Barr. Coalgebras in a category of algebras. D.A. Buchsbaum. Lectures on Regular Local Rings. R. Fittler. Categories of modules with initial objects. J.F. Kennison. Coreflection maps which resemble universal coverings. J. Lambek. Deductive systems and categories (II). S. MacLane. Possible programs...
Springer-Verlag, London, Limited, 2012. — 320 p. — (Algebra and Applications 17) — ISBN: 1447122933. The most important invariant o a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far...
De Gruyter, 2023. — 436 p. — ISBN 978-3-11-108056-7. This book presents the formal definition of fundamental transformations in Category Theory as a mathematical language to be used in Computer Science modelling. The book focuses in particular on models with Global and Internal symmetries (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second...
Elsevier, 2008. — 310 p. — (Studies in Logic and the Foundations of Mathematics 152). Contents. Introduction. Partial Combinatory Algebras. Realizability triposes and toposes. The Effective Topos. Variations.
Springer/Birkhauser, 2025. — 301 p. — (Computer Science Foundations and Applied Logic). — ISBN 978-3-031-68537-8. This unique book offers an introductory course on category theory, which became a working language in algebraic geometry and number theory in the 1950s and began to spread to logic and Computer Science soon after it was created. Offering excellent use of helpful...
Cambridge: Cambridge University Press, 2025. — 668 p. This is the first book to revisit the theory of rewriting in the context of strict higher categories, through the unified approach provided by polygraphs, and put it in the context of homotopical algebra. The first half explores the theory of polygraphs in low dimensions and its applications to the computation of the...
Cambridge University Press, 2000. 361 pages. Contents. Categories. Categories and Exact Sequences. Change of Rings. The Morita Theory. Limits in Categories. Localization. Local-Global Methods.
Springer, 1966. — xviii + 562 p. — ISBN13: 978-3-642-99904-8, e-ISBN13: 978-3-642-99902-4. This volume contains the articles contributed to the Conference on Categorical Algebra, held June 7—12, 1965, at the San Diego campus of the University of California under the sponsorship of the United States Air Force Office of Scientific Research. Of the thirty-seven mathematicians, who...
University of Southern California, 2018. — 129 p. Abstract iIntroduction Categorification and Decategorification Categorification Diagrammatic Categories Trace Decategorification Heisenberg Algebras and Heisenberg Categories Heisenberg Algebra Heisenberg Category Endomorphism spaces of H H as Categorified Induction and Restriction Twisted Heisenberg Algebra Twisted Heisenberg...
München: Ludwig-Maximilians-Universität (LMU), 2004. — 90 p. Introduction. Foundations. Graphs. Monoids. Categories. Constructions on categories. Functors. Special types of functors. Natural transformations. Representable functors and the Yoneda Lemma. Representable functors. Terminal and initial objects. The extension principle. Isomorphisms. Monomorphisms and epimorphisms....
Singapore: World Scientific, 2001. — 238 p. An exposition of building blocks for deformation theory of braided monoidal categories, giving rise to sequences of Vasseliv invariants of framed links, clarifying the interrelations between them.
Birkhauser, 2021. — 300 p. — (Compact Textbooks in Mathematics). — ISBN 978-3030615239. This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics. It treats the basics of the theory and supplies all the necessary details while leading the reader along a streamlined path from the basic definitions to more...
Berlin: Springer-Verlag, 1974. — 118 p. Iterated loop spaces The inclusion X→ΩnΣnX The map Fn(X) → ΩFn−1(ΣX) The cohomology of the Fn The structure of iterated loop spaces in the metastable range An unstable adams spectral sequence The loop space functor for resolutions The metastable exact sequence Calculating the groups Open image in new window Calculations of the stable...
М.: Инфра-М, 2017. — 174 с. В монографии излагается теория категорий первого порядка и строгих высших категорий. Особое внимание уделено ситуациям конкретного сопряжения и конкретной двойственности высшего порядка. Вводятся новые примеры конкретной двойственности, такие как: двойственность А.M. Виноградова, 2-двойственность Гельфанда — Наймарка, двойственность Понтрягина —...
Уважаемые: администратор, модераторы, доверенные пользователи, а также все те, которые участвовали в работе по созданию нового подраздела - Теория категорий: Сергей&Бал, muzteoretik, Petrovych, DosiaHeDeine, и многие, многие др... Я сердечно благодарен Вам за то, что Вы, несмотря на праздники Нового года и великую занятость, откликнулись на эту нужду и создали этот подраздел. Слава Богу! Теперь у нас у всех есть где систематизировать нужную литературу по Теории категорий. Да благословит Господь Вас, ваших родных, близких, друзей и знакомых. С уважением, благодарностью и благословением,
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Я сердечно благодарен Вам за то, что Вы, несмотря на праздники Нового года и великую занятость, откликнулись на эту нужду и создали этот подраздел. Слава Богу! Теперь у нас у всех есть где систематизировать нужную литературу по Теории категорий.
Да благословит Господь Вас, ваших родных, близких, друзей и знакомых.
С уважением, благодарностью и благословением,