An ABC of Category Theory

Autumn 2004

 

This course is aimed at potential users of categorical ideas rather than aspiring category theorists. I will skip details wherever I can.

There will not be many useful theorems in the course. Rather, the point is to teach you how to think categorically. To this end, I will set a couple of exercises each week, and I strongly suggest that you do them: otherwise, the point is likely to be lost. (I know authors always say "the exercises are an essential part of the text", but I really think it's true here.)

0 Informal introduction
(handout, not a live performance: pdf, ps; solutions to exercises: pdf, ps)
1 Categories and functors
(notes: pdf, ps; solutions to exercises: pdf, ps)
2 Natural transformations and equivalence
(notes: pdf, ps; solutions to exercises: pdf, ps)
3 Adjoints
(notes: pdf, ps; solutions to exercises: pdf, ps)
4 Representability
(notes: pdf, ps; solutions to exercises: pdf, ps)
5 Limits
(notes: pdf, ps; solutions to exercises: pdf, ps)
6 Adjoints, representables and limits
(notes: pdf, ps; solutions to exercises: pdf, ps)
7 Monads
(notes: pdf, ps; solutions to exercises: pdf, ps)
8 Monoidal categories
(notes: pdf, ps; solutions to exercises: pdf, ps)

Here is the page for another category theory course that I gave, more detailed than this one.

 
This page was last modified on 13 December 2004.