Monoidal Category Theory: Unifying Concepts in Mathematics, Physics, and Computing

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Noson S. Yanofsky

Monoidal Category Theory

Unifying Concepts in Mathematics, Physics, and Computing

Noson S. Yanofsky

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English

MIT Press
10 December 2024

Mathematics & Sciences; Computing: general

A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences.

A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences.

Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theorydemonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before progressing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many.

Makes category theory accessible to non-math majors Uses easy-to-understand language and emphasizes diagrams over equations Incremental, iterative approach eases students into advanced concepts A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory Extensive exercises and examples demonstrate the broad range of applications of categorical structures

Modular structure allows instructors to fit text to the needs of different courses

Instructor resources include slides

By: Noson S. Yanofsky
Imprint: MIT Press
Country of Publication: United States
Dimensions: Height: 244mm, Width: 170mm,
Weight: 567g
ISBN: 9780262049399
ISBN 10: 0262049392
Pages: 672
Publication Date: 10 December 2024
Audience: General/trade , ELT Advanced
Format: Hardback
Publisher's Status: Active

Preface 1 Introduction 1 2 Categories 39 3 StructuresWithin Categories 99 4 Relationships Between Categories 161 5 Monoidal Categories 251 6 Relationships Between Monoidal Categories 311 7 Variations of Monoidal Categories 365 8 Describing Structures 419 9 Advanced Topics 487 10 More Mini-Courses 579 Appendix A: Venn Diagrams 637 Appendix B: Index of Categories 645 Appendix C: Suggestions for Further Study 653 Appendix D: Answers to Selected Problems 657 Bibliography 658 Index 679

Noson S. Yanofsky is Professor of Computer and Information Science at Brooklyn College and The Graduate Center, CUNY, and author, most recently, of Theoretical Computer Science for the Working Category Theorist, among other books.