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An Invitation to Applied Category Theory
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Table 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.

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

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.

Reviews

'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
'The authors quite rightly describe category theory as a tool for thinking. So if your work requires thinking, this book is for you.' Bartosz Milewski, author of Category Theory for Programmers
'This book provides a fantastic introduction to how category is not just abstract nonsense but can be applied to real-world engineering problems, pedagogical while still broad, and fun. A must read for all those entering the exciting emerging field of applied category theory by two key players of this community.' Bob Coecke, University of Oxford
'An invitation to Applied Category Theory: Seven Sketches in Compositionality provides a grand tour of the fascinating emergent field of applied category theory that centers examples and use cases before gently introducing the accompanying abstract notions. Fong and Spivak should be congratulated for providing this accessible broad viewpoint to illustrate what category theory is all about vis-a-vis the real world.' Emily Riehl, The Johns Hopkins University
`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
`The authors quite rightly describe category theory as a tool for thinking. So if your work requires thinking, this book is for you.' Bartosz Milewski, author of Category Theory for Programmers
`This book provides a fantastic introduction to how category is not just abstract nonsense but can be applied to real-world engineering problems, pedagogical while still broad, and fun. A must read for all those entering the exciting emerging field of applied category theory by two key players of this community.' Bob Coecke, University of Oxford
`An invitation to Applied Category Theory: Seven Sketches in Compositionality provides a grand tour of the fascinating emergent field of applied category theory that centers examples and use cases before gently introducing the accompanying abstract notions. Fong and Spivak should be congratulated for providing this accessible broad viewpoint to illustrate what category theory is all about vis-a-vis the real world.' Emily Riehl, The Johns Hopkins University

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