Category Theory

What is this?

These are a set of notes on category theory I worked on for my latter two years as a mathematics undergraduate. It covers many different areas of category theory, contains many examples in pure mathematics, and has hundreds of original mathematical diagrams.

This is the html version. If you'd like the original LaTeX PDF version, see here. In PDF format, it totals to over 400 pages.

Motivation

Category Theory is a very beautiful area of mathematics that unites different areas of mathematics, in particular algebra and topology. The field attempts to discover patterns and relationships between seemingly different mathematical constructions, and it came about as a field when algebraic topologists wanted to associate topological spaces with algebraic groups, since this was useful, but they had no formal way of describing this process.

My goal with these notes was to read most of the classic texts in category theory and then find the most intuitive way to explain and illustrate the concepts that I learned for the benefit of others. Many category theory texts are often quite cryptic and terse, so I figured I could save people some time in understanding these concepts with these notes.

I relied heavily on Categories for the Working Mathematician, the de facto category theory text which is great but is extremely terse and challenging.