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Author : Emily Riehl,Dominic Verity
Publisher : Cambridge University Press
Page : 781 pages
File Size : 51,8 Mb
Release : 2022-02-10
Category : Mathematics
ISBN : 9781108837989
This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.
Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 42,8 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820804
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 : Tom Leinster
Publisher : Cambridge University Press
Page : 193 pages
File Size : 51,6 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9781107044241
A short introduction ideal for students learning category theory for the first time.
Author : Gregory Maxwell Kelly
Publisher : CUP Archive
Page : 260 pages
File Size : 42,6 Mb
Release : 1982-02-18
Category : Mathematics
ISBN : 0521287022
Author : Emily Riehl
Publisher : Cambridge University Press
Page : 371 pages
File Size : 42,9 Mb
Release : 2014-05-26
Category : Mathematics
ISBN : 9781107048454
This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.
Author : Benjamin C. Pierce
Publisher : MIT Press
Page : 117 pages
File Size : 50,6 Mb
Release : 1991-08-07
Category : Computers
ISBN : 9780262326452
Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. 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 provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading
Author : Birgit Richter
Publisher : Cambridge University Press
Page : 401 pages
File Size : 53,7 Mb
Release : 2020-04-16
Category : Mathematics
ISBN : 9781108479622
Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.
Author : David I. Spivak
Publisher : MIT Press
Page : 495 pages
File Size : 40,8 Mb
Release : 2014-10-17
Category : Mathematics
ISBN : 9780262320535
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 and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
Author : Steve Awodey
Publisher : Oxford University Press
Page : 328 pages
File Size : 49,8 Mb
Release : 2010-06-17
Category : Mathematics
ISBN : 9780199587360
A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.
Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 54,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475747218
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 of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Author : G.M. Kelly
Publisher : Springer
Page : 386 pages
File Size : 53,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540372707
Author : Michael Barr,Charles Wells
Publisher : Unknown
Page : 352 pages
File Size : 44,9 Mb
Release : 1995
Category : Computers
ISBN : UOM:39015034447873
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 : Harold Simmons
Publisher : Cambridge University Press
Page : 128 pages
File Size : 50,8 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 9781139503327
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 postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.
Author : Andrea Asperti,Giuseppe Longo
Publisher : MIT Press (MA)
Page : 330 pages
File Size : 49,8 Mb
Release : 1991
Category : Computers
ISBN : UOM:39015022019742
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.
Author : F. William Lawvere,Robert Rosebrugh
Publisher : Cambridge University Press
Page : 280 pages
File Size : 55,5 Mb
Release : 2003-01-27
Category : Mathematics
ISBN : 0521010608
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.