Category Theory in Context

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Category Theory in Context

Category Theory in Context

  • Author: Emily Riehl
  • Publisher: Courier Dover Publications
  • ISBN: 0486820807
  • Category: Mathematics
  • Page: 272
  • View: 853
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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.

Category Theory

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Category Theory

Category Theory

  • Author: Steve Awodey
  • Publisher: Oxford University Press
  • ISBN: 0191513822
  • Category: Mathematics
  • Page: 256
  • View: 5912
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This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. 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 it assumes 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.

What is Category Theory?

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What is Category Theory?

What is Category Theory?

  • Author: Giandomenico Sica
  • Publisher: Polimetrica s.a.s.
  • ISBN: 8876990313
  • Category: Mathematics
  • Page: 290
  • View: 6912
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Category Theory at Work

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Category Theory at Work

Category Theory at Work

  • Author: Horst Herrlich
  • Publisher: N.A
  • ISBN: N.A
  • Category: Categories (Mathematics)
  • Page: 395
  • View: 8718
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Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada

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Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada

Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada

Proceedings of an International Summer Category Theory Meeting, Held June 23-30, 1991

  • Author: Robert Andrew George Seely,American Mathematical Society,Québec) International Summer Category Theory Meeting (1991 : Montréal,Canadian Mathematical Society
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821860182
  • Category: Mathematics
  • Page: 447
  • View: 6141
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As category theory approaches its first half-century, it continues to grow, finding new applications in areas that would have seemed inconceivable a generation ago, as well as in more traditional areas. The language, ideas, and techniques of category theory are well suited to discovering unifying structures in apparently different contexts. Representing this diversity of the field, this book contains the proceedings of an international conference on category theory. The subjects covered here range from topology and geometry to logic and theoretical computer science, from homotopy to braids and conformal field theory. Although generally aimed at experts in the various fields represented, the book will also provide an excellent opportunity for nonexperts to get a feel for the diversity of current applications of category theory.

Basic Category Theory for Computer Scientists

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Basic Category Theory for Computer Scientists

Basic Category Theory for Computer Scientists

  • Author: Benjamin C. Pierce,Benjamin C. (Professor Pierce, University of Pennsylvania),Benjamin C.. Pierce
  • Publisher: MIT Press
  • ISBN: 9780262660716
  • Category: Computers
  • Page: 100
  • View: 8110
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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

Category Theory for the Sciences

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Category Theory for the Sciences

Category Theory for the Sciences

  • Author: David I. Spivak
  • Publisher: MIT Press
  • ISBN: 0262028131
  • Category: Computers
  • Page: 486
  • View: 9587
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An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences.

Category Theory and Applications

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Category Theory and Applications

Category Theory and Applications

A Textbook for Beginners

  • Author: Marco Grandis
  • Publisher: World Scientific
  • ISBN: 9813231084
  • Category:
  • Page: 304
  • View: 7216
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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 first course in Category Theory. It covers its basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications. Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications and a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields. Contents: IntroductionCategories, Functors and Natural TransformationsLimits and ColimitsAdjunctions and MonadsApplications in AlgebraApplications in Topology and Algebraic TopologyApplications in Homological AlgebraHints at Higher Dimensional Category TheoryReferencesIndices Readership: Graduate students and researchers of mathematics, computer science, physics. Keywords: Category TheoryReview: Key Features: The main notions of Category Theory are presented in a concrete way, starting from examples taken from the elementary part of well-known disciplines: Algebra, Lattice Theory and TopologyThe theory is developed presenting other examples and some 300 exercises; the latter are endowed with a solution, or a partial solution, or adequate hintsThree chapters and some extra sections are devoted to applications

Tool and Object

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Tool and Object

Tool and Object

A History and Philosophy of Category Theory

  • Author: Ralph Krömer
  • Publisher: Springer Science & Business Media
  • ISBN: 3764375248
  • Category: Mathematics
  • Page: 367
  • View: 1577
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Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

Basic Category Theory

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Basic Category Theory

Basic Category Theory

  • Author: Tom Leinster
  • Publisher: Cambridge University Press
  • ISBN: 1107044243
  • Category: Mathematics
  • Page: 190
  • View: 312
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A short introduction ideal for students learning category theory for the first time.