Invitation to Applied Category Theory - Seven Sketches in Compositionality

Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.

List of contents

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.

About the author

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.David I. Spivak is a research scientist in the Department of Mathematics at the Massachusetts Institute of Technology. He has found applications of category theory ranging from database integration to knowledge representation, from materials science to dynamical systems and behaviour. He is the author of two other books in category theory.

Summary

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.

Product details

• Authors: Brendan Fong, Brendan (Massachusetts Institute of Technolo Fong, Brendan (Massachusetts Institute of Technology) Fong, David I. Spivak, David I. (Massachusetts Institute of Technology) Spivak, Spivak David I.
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.08.2019
• EAN: 9781108482295
• ISBN: 978-1-108-48229-5
• No. of pages: 348
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; Software Engineering, MATHEMATICS / Logic, Quantum physics (quantum mechanics & quantum field theory), Quantum physics (quantum mechanics and quantum field theory), Mathematical logic