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An Invitation to Applied Category Theory
  • Publisher: Cambridge University Press
  • Expected online publication date: July 2019
  • Print publication year: 2019
  • Online ISBN: 9781108668804

Book description

Category 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 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-à-vis the real world.'

Emily Riehl - The Johns Hopkins University


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