Category Theory in Context

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.