Category Theory


Author: Steve Awodey

Publisher: Oxford University Press

ISBN: 0191513822

Category: Mathematics

Page: 256

View: 4687

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.

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: 1330

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.

What is Category Theory?


Author: Giandomenico Sica

Publisher: Polimetrica s.a.s.

ISBN: 8876990313

Category: Mathematics

Page: 290

View: 2225

Category Theory in Context


Author: Emily Riehl

Publisher: Courier Dover Publications

ISBN: 0486820807

Category: Mathematics

Page: 272

View: 1660

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 at Work


Author: Horst Herrlich,Hans-Eberhard Porst

Publisher: N.A


Category: Categories (Mathematics)

Page: 395

View: 5525

Basic Category Theory for Computer Scientists


Author: Benjamin C. Pierce,Benjamin C. (Professor Pierce, University of Pennsylvania),Benjamin C.. Pierce,Michael R. Garey,Albert Meyer

Publisher: MIT Press

ISBN: 9780262660716

Category: Computers

Page: 100

View: 3612

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

Categories, Types and Data Structures

An Introduction to Category Theory for the Working Computer Scientist


Author: Andréa Asperti,G. Longo

Publisher: MIT Press (MA)

ISBN: 9780262011259

Category: Computers

Page: 306

View: 4149

Higher Category Theory

Workshop on Higher Category Theory and Physics, March 28-30, 1997, Northwestern University, Evanston, IL


Author: Ezra Getzler,Mikhail M. Kapranov

Publisher: American Mathematical Soc.

ISBN: 0821810561

Category: Mathematics

Page: 134

View: 8830

This volume presents the proceedings of the workshop on higher category theory and mathematical physics held at Northwestern University. Exciting new developments were presented with the aim of making them better known outside the community of experts. In particular, presentations in the style, 'Higher Categories for the Working Mathematician', were encouraged. The volume is the first to bring together developments in higher category theory with applications. This collection is a valuable introduction to this topic - one that holds great promise for future developments in mathematics.

Basic Category Theory


Author: Tom Leinster

Publisher: Cambridge University Press

ISBN: 1107044243

Category: Mathematics

Page: 190

View: 9961

A short introduction ideal for students learning category theory for the first time.

Category Theory and Computer Science

Paris, France, September 3-6, 1991. Proceedings


Author: David H. Pitt,Pierre-Louis Curien,Samson Abramsky,Andrew Pitts,Axel Poigne,David E. Rydeheard

Publisher: Springer Science & Business Media

ISBN: 9783540544951

Category: Mathematics

Page: 304

View: 8914

The papers in this volume were presented at the fourth biennial Summer Conference on Category Theory and Computer Science, held in Paris, September3-6, 1991. Category theory continues to be an important tool in foundationalstudies in computer science. It has been widely applied by logicians to get concise interpretations of many logical concepts. Links between logic and computer science have been developed now for over twenty years, notably via the Curry-Howard isomorphism which identifies programs with proofs and types with propositions. The triangle category theory - logic - programming presents a rich world of interconnections. Topics covered in this volume include the following. Type theory: stratification of types and propositions can be discussed in a categorical setting. Domain theory: synthetic domain theory develops domain theory internally in the constructive universe of the effective topos. Linear logic: the reconstruction of logic based on propositions as resources leads to alternatives to traditional syntaxes. The proceedings of the previous three category theory conferences appear as Lecture Notes in Computer Science Volumes 240, 283 and 389.