Math 727: Category Theory in Context


An introduction to categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, and other topics as time permits with the aim of revisiting a broad range of mathematical examples from the categorical perspective. I hope to explain how to calculate the free product of groups, rings, and other algebraic objects as well as why “all concepts are Kan extensions.”


The course will meet on Mondays and Wednesdays from 9-10:15am in Krieger 312. The syllabus can be found here.

My office hours will be held on Mondays from 3-4pm, immediately after class, or by appointment.


The primary text will be comprised of lecture notes, now published by Dover Publications, which may be found here.


For those seeking supplemental reading, I recommend Basic Category Theory by Tom Leinster, also available on the arXiv, or the classic Categories for the Working Mathematician.


If you have any questions about the course, please get in touch. My contact info can be found on my personal website.