# 1. The Brower Fixed-Point Theorem

### đźŽ‰đźŽ‰đźŽ‰ Welcome to Algebraic Topology I đźŽ‰đźŽ‰đźŽ‰

In this first lecture we give a brief introduction to the â€śideaâ€ť of algebraic topology, and illustrate the concept by giving a â€śproofâ€ť of the Brower Fixed Point Theorem. (I say â€śproofâ€ť because the proof uses the homology, which we won't start for a few more lectures ...)

We then give the first few elementary definitions in Category Theory. My plan is to stealthily introduce a little bit of abstract nonsense each lecture, so that by the end of the course you will know lots without ever having been completely overwhelmed.

To â€śmotivateâ€ť you to learn more category theory, have a read of this (by Ed Morehouse). The more category theory you know, the funnier it will beâ€”eventually you will no doubt be unable to read it without laughing hysterically (okay, maybe that's just me ...)

##### Warning

My lecture notes likely have one or two (million) typos in them. Please leave a comment if you spot something wrong and I will fix it! I encourage you *not* to print the notes out just yet, since I'll probably edit them at least six times over the next few days (hopefully in a week or so they should be relatively stable ...)

Comments and questions?