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Author : Gregory Maxwell Kelly
Publisher : CUP Archive
ISBN 13 : 9780521287029
Total Pages : 260 pages
Book Rating : 4.2/5 (87 download)
Download or read book Basic Concepts of Enriched Category Theory written by Gregory Maxwell Kelly and published by CUP Archive. This book was released on 1982-02-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Emily Riehl
Publisher : Cambridge University Press
ISBN 13 : 1139952633
Total Pages : 371 pages
Book Rating : 4.1/5 (399 download)
Download or read book Categorical Homotopy Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2014-05-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Author : Tom Leinster
Publisher : Cambridge University Press
ISBN 13 : 1107044243
Total Pages : 193 pages
Book Rating : 4.1/5 (7 download)
Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.
Author : Eduardo J. Dubuc
Publisher : Springer
ISBN 13 : 3540363076
Total Pages : 190 pages
Book Rating : 4.5/5 (43 download)
Download or read book Kan Extensions in Enriched Category Theory written by Eduardo J. Dubuc and published by Springer. This book was released on 2006-11-15 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original purpose of this paper was to provide suitable enriched completions of small enriched categories.
Author : Birgit Richter
Publisher : Cambridge University Press
ISBN 13 : 1108847625
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)
Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
Author : Emily Riehl
Publisher : Courier Dover Publications
ISBN 13 : 0486820807
Total Pages : 272 pages
Book Rating : 4.4/5 (868 download)
Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Author : Emily Riehl
Publisher : Cambridge University Press
ISBN 13 : 1108952194
Total Pages : 782 pages
Book Rating : 4.1/5 (89 download)
Download or read book Elements of ∞-Category Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2022-02-10 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.
Author : Brendan Fong
Publisher : Cambridge University Press
ISBN 13 : 1108582249
Total Pages : 351 pages
Book Rating : 4.1/5 (85 download)
Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.
Author : Fosco Loregian
Publisher : Cambridge University Press
ISBN 13 : 1108746128
Total Pages : 331 pages
Book Rating : 4.1/5 (87 download)
Download or read book (Co)end Calculus written by Fosco Loregian and published by Cambridge University Press. This book was released on 2021-07-22 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.
Author : Bartosz Milewski
Publisher :
ISBN 13 : 9780464243878
Total Pages : pages
Book Rating : 4.2/5 (438 download)
Download or read book Category Theory for Programmers (New Edition, Hardcover) written by Bartosz Milewski and published by . This book was released on 2019-08-24 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 in relatively simple terms to anybody with some experience in programming.That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.
Author : John C. Baez
Publisher : Springer Science & Business Media
ISBN 13 : 1441915362
Total Pages : 292 pages
Book Rating : 4.4/5 (419 download)
Download or read book Towards Higher Categories written by John C. Baez and published by Springer Science & Business Media. This book was released on 2009-09-24 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Author : Ash Asudeh
Publisher : Oxford Studies in Semantics an
ISBN 13 : 0198847858
Total Pages : 202 pages
Book Rating : 4.1/5 (988 download)
Download or read book Enriched Meanings written by Ash Asudeh and published by Oxford Studies in Semantics an. This book was released on 2020 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a theory of enriched meanings for natural language interpretation that uses the concept of monads and related ideas from category theory, a branch of mathematics that has been influential in theoretical computer science and elsewhere. Certain expressions that exhibit complex effects at the semantics/pragmatics boundary live in an enriched meaning space, while others live in a more basic meaning space. These basic meanings are mapped to enriched meanings only when required compositionally, which avoids generalizing meanings to the worst case. Ash Asudeh and Gianluca Giorgolo show that the monadic theory of enriched meanings offers a formally and computationally well-defined way to tackle important challenges at the semantics/pragmatics boundary. In particular, they develop innovative monadic analyses of three phenomena - conventional implicature, substitution puzzles, and conjunction fallacies - and demonstrate that the compositional properties of monads model linguistic intuitions about these cases particularly well. The analyses are accompanied by exercises to aid understanding, and the computational tools used are available on the book's companion website. The book also contains background chapters on enriched meanings and category theory. The volume is interdisciplinary in nature, with insights from semantics, pragmatics, philosophy of language, psychology, and computer science, and will appeal to graduate students and researchers from a wide range of disciplines with an interest in natural language understanding and representation.
Author : Michael Barr
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.3/5 (91 download)
Download or read book Category Theory for Computing Science written by Michael Barr and published by . This book was released on 1995 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.
Author : Elaine M. Landry
Publisher : Oxford University Press
ISBN 13 : 019874899X
Total Pages : 486 pages
Book Rating : 4.1/5 (987 download)
Download or read book Categories for the Working Philosopher written by Elaine M. Landry and published by Oxford University Press. This book was released on 2017 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on category theory for a broad philosophical readership. There is no other discussion of category theory comparable in its scope. It is designed to show the interest and significant of category theory for philosophers working in a range of areas, including mathematics, proof theory, computer science, ontology, physics, biology, cognition, mathematical modelling, the structure of scientific theories, and the structure of the world. Moreover, it does this in a way that is accessible to non specialists. Each chapter is written by either a category-theorist or a philosopher working in one of the represented fields, in a way that builds on the concepts already familiar to philosophers working in these areas. The book is split into two halves. The 'pure' chapters focus on the use of category theory for mathematical, foundational, and logical purposes, while the 'applied' chapters consider the use of category theory for representational purposes, investigating category theory as a framework for theories of physics and biology, for mathematical modelling more generally, and for the structure of scientific theories. Book jacket.
Author : Jacob Lurie
Publisher : Princeton University Press
ISBN 13 : 1400830559
Total Pages : 944 pages
Book Rating : 4.4/5 (8 download)
Download or read book Higher Topos Theory (AM-170) written by Jacob Lurie and published by Princeton University Press. This book was released on 2009-07-06 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.
Author : Dirk Hofmann
Publisher : Cambridge University Press
ISBN 13 : 1107063949
Total Pages : 523 pages
Book Rating : 4.1/5 (7 download)
Download or read book Monoidal Topology written by Dirk Hofmann and published by Cambridge University Press. This book was released on 2014-07-31 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.
Author : Andrea Asperti
Publisher : MIT Press (MA)
ISBN 13 :
Total Pages : 330 pages
Book Rating : 4.3/5 (91 download)
Download or read book Categories, Types, and Structures written by Andrea Asperti and published by MIT Press (MA). This book was released on 1991 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 context of programming language design.
