Category theory provides a cross-disciplinary language for mathematics designed to delineate general phenomena, which enables the transfer of ideas from one area of study to another.

Category theory has provided the foundations for many of the twentieth century's most significant advances in pure mathematics. This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities.

The treatment introduces the essential concepts of category theory:

• Categories, functors, natural transformations
• The Yoneda lemma, limits and colimits
• Adjunctions, monads, and other topics

Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in the following:

• Algebra, number theory
• Algebraic geometry, and algebraic topology
• Prerequisites are limited to familiarity with some basic set theory and logic

Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas.

Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen (Set Theory and the Continuum Hypothesis), Alfred Tarski (Undecidable Theories), Gary Chartrand (Introductory Graph Theory), Hermann Weyl (The Concept of a Riemann Surface), Shlomo Sternberg (Dynamical Systems), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.

Table of Contents

Chapter 1. Categories, Functors, Natural Transformations

Chapter 2. Universal Properties, Representability, and the Yoneda Lemma

Chapter 3. Limits and Colimits

Chapter 4. Adjunctions

Chapter 5. Monads and their Algebras

Chapter 6. All Concepts are Kan Extensions

Epilogue: Theorems in Category Theory

About the Author

Emily Riehl is Assistant Professor in the Department of Mathematics at Johns Hopkins University. She received her Ph.D. from the University of Chicago in 2011 and was a Benjamin Pierce and NSF Postdoctoral Fellow at Harvard University from 2011–15. She is also the author of Categorical Homotopy Theory.