Brendan Fong

Invitation to Applied Category Theory (eBook, PDF)

Seven Sketches in Compositionality

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 18. Juli 2019
• Englisch
• ISBN-13: 9781108621854
• Artikelnr.: 66178673

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