Description
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
Table of Contents
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
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