Brendan Fong, David I. Spivak

An Invitation to Applied Category Theory

Seven Sketches in Compositionality

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 348
• Erscheinungstermin: 18. Juli 2019
• Englisch
• Abmessung: 246mm x 175mm x 22mm
• Gewicht: 678g
• ISBN-13: 9781108711821
• ISBN-10: 1108711820
• Artikelnr.: 55194007

Autorenporträt

Brendan Fong is a postdoctoral associate in the Department of Mathematics at the Massachusetts Institute of Technology. His research explores how we use pictures to represent and reason about the systems around us, and how to understand the world from a relational point of view. These topics find their intersection in applied category theory.

Inhaltsangabe

Preface; 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.

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Preface
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.

Rezensionen

'Category 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