Category Theory

Catalog description

Category theory is the rigorous study of the consequences of taking the notation of an arrow for a function seriously. Instead of emphasizing that a function has variables to evaluate via a formula, category theory posits that the most important features of how we use functions are governed by the axioms for composition and the consequences of those axioms. Category theory has roots in algebraic topology and homological algebra, but also has deep connections with topics as diverse as algebraic geometry, logic, and metric spaces. The goal of this course is to give students an introduction to category theory an an independent subject of study. As such, this course will view category theory as a kind of algebra, and so familiarity with other algebraic structures (groups, rings, vector spaces), good proof-writing technique, and comfort with a high degree of abstraction are the primary prerequisites. Examples from a wide variety of other areas of mathematics will be given throughout, but no subject-specific knowledge from these areas will be required. Prereq: Graduate Student standing or MATH 308 or MATH 309 .