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Invitation to Applied Category Theory : Seven Sketches in Compositionality by David I. Spivak and Brendan Fong (2019, Trade Paperback)

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About this product

Product Identifiers

PublisherCambridge University Press

ISBN-101108711820

ISBN-139781108711821

eBay Product ID (ePID)24038541708

Product Key Features

Number of Pages348 Pages

Publication NameInvitation to Applied Category Theory : Seven Sketches in Compositionality

LanguageEnglish

SubjectGroup Theory, Logic, Mathematical Analysis

Publication Year2019

TypeTextbook

AuthorDavid I. Spivak, Brendan Fong

Subject AreaMathematics

FormatTrade Paperback

Dimensions

Item Height0.7 in

Item Weight23.9 Oz

Item Length9.7 in

Item Width6.8 in

Additional Product Features

Intended AudienceScholarly & Professional

ReviewsCategory theory was always applied, but traditionally within pure mathematics. Now it is being used to clarify and synthesize a broad range of topics outside mathematics: from computer science to linguistics, from quantum theory to chemistry, and beyond. Charmingly informal yet crystal clear, Fong and Spivak's book does a wonderful job of demonstrating the power of category theory to beginners - even beginners without much background in pure mathematics. John Baez, University of California, Riverside

TitleLeadingAn

Dewey Edition23

IllustratedYes

Dewey Decimal512/.62

Table Of ContentPreface; 1. Generative effects: orders and Galois connections; 2. Resource theories: monoidal preorders and enrichment; 3. Databases: categories, functors, and universal constructions; 4. Collaborative design: profunctors, categorification, and monoidal categories; 5. Signal flow graphs: props, presentations, and proofs; 6. Electric circuits: hypergraph categories and operads; 7. Logic of behavior: sheaves, toposes, and internal languages; Appendix. Exercise solutions; References; Index.

SynopsisCategory 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., Category theory reveals commonalities between structures of all sorts. This self-contained tour of applied category theory shows its potential in science, engineering, and beyond. Each chapter discusses a real-world application using category-theoretic tools, all of which are introduced in an accessible way with many examples and exercises.

LC Classification NumberQA9.25.F66 2019