Invitation to Applied Category Theory

Invitation to Applied Category Theory

Seven Sketches in Compositionality

Fong, Brendan (Massachusetts Institute of Technology); Spivak, David I. (Massachusetts Institute of Technology)

Cambridge University Press

07/2019

348

Dura

Inglês

9781108482295

15 a 20 dias

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.
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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