Category Theory
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Category Theory In Context
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Author : Emily Riehl
language : en
Publisher: Courier Dover Publications
Release Date : 2016-11-16
Category Theory In Context written by Emily Riehl and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Mathematics categories.
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 course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, and other topics. Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. Prerequisites are limited to familiarity with some basic set theory and logic.
Category Theory
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Author : Steve Awodey
language : en
Publisher: OUP Oxford
Release Date : 2010-06-18
Category Theory written by Steve Awodey and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-18 with Philosophy categories.
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, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists! This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.
An Introduction To Category Theory
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Author : Harold Simmons
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-22
An Introduction To Category Theory written by Harold Simmons and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-22 with Mathematics categories.
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.
An Introduction To Category Theory
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Author : Viakalathur Sankrithi Krishnan
language : en
Publisher: North-Holland
Release Date : 1981
An Introduction To Category Theory written by Viakalathur Sankrithi Krishnan and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Category Theory Using Haskell
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Author : Shuichi Yukita
language : en
Publisher: Springer Nature
Release Date : 2024-12-06
Category Theory Using Haskell written by Shuichi Yukita and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-06 with Computers categories.
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, the work covers (among other things) concepts of functors, natural transformations, monads, adjoints, universality, category equivalence, and many others. The main goal is to understand the Yoneda lemma, which can be used to reverse-engineer the implementation of a function. Later chapters offer more insights into computer science, including computation with output, nondeterministic computation, and continuation passing. Topics and features: Contains rigorous mathematical arguments to support the theory Provides numerous Haskell code-implementing examples Engages with plentiful diagram chasing, with special emphasis on the design patterns for constructing a large diagram out of basic small pieces Offers insights into category theory to quantum computing and the foundation of computing discipline Serves as a preparatory course for monoidal categories and higher categories The work will be useful to undergraduate students in computer science who have enough background in college mathematics such as linear algebra and basics in Haskell polymorphic functions. Further, it will appeal to graduate students and researchers in computing disciplines who want to newly acquire serious knowledge of category theory.
What Is Category Theory
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Author : Giandomenico Sica
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2006
What Is Category Theory written by Giandomenico Sica and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Basic Category Theory For Computer Scientists
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Author : Benjamin C. Pierce
language : en
Publisher: MIT Press
Release Date : 1991-08-07
Basic Category Theory For Computer Scientists written by Benjamin C. Pierce and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-08-07 with Computers categories.
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
Monoidal Category Theory
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Author : Noson S. Yanofsky
language : en
Publisher: MIT Press
Release Date : 2024-11-05
Monoidal Category Theory written by Noson S. Yanofsky and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Computers categories.
A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences. Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theorydemonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before progressing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many. Makes category theory accessible to non-math majors Uses easy-to-understand language and emphasizes diagrams over equations Incremental, iterative approach eases students into advanced concepts A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory Extensive exercises and examples demonstrate the broad range of applications of categorical structures Modular structure allows instructors to fit text to the needs of different courses Instructor resources include slides
Higher Category Theory
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Author : Ezra Getzler
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Higher Category Theory written by Ezra Getzler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Comprises six presentations on new developments in category theory from the March 1997 workshop. The topics are categorification, computads for finitary monads on globular sets, braided n- categories and a-structures, categories of vector bundles and Yang- Mills equations, the role of Michael Batanin's monoidal globular categories, and braided deformations of monoidal categories and Vassiliev invariants. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
Category Theory 1991 Proceedings Of The 1991 Summer Category Theory Meeting Montreal Canada
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Author : Robert Andrew George Seely
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Category Theory 1991 Proceedings Of The 1991 Summer Category Theory Meeting Montreal Canada written by Robert Andrew George Seely and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Twenty-seven papers address applications of category theory in new domains as well as in its traditional contexts. Among the topics: a Stone duality for metric spaces; sheaves in cocomplete categories; completeness in continuity spaces; dualities for accessible categories; some problems in descriptive locale theory; modeling homotopy coherence; and functorial selection of morphisms. No index. Annotation copyright by Book News, Inc., Portland, OR