/sci/ - Science & Math

Hello /sci/, and welcome to the second lecture in my Brave New Algebra series. Today we will be discussing category theory. This won't be as careless as yesterday's lecture, but it is NOT going to be super duper careful either. You've been warned. All of this stuff has been fully formalized and carefully handled in a variety of great textbooks (Categories for the Working Mathematician by Mac Lane is pretty good). This lecture is meant to familiarize people with the language and methods of category theory. My goal is not a starkly rigorous handling. With that said, let's begin.

I will be fixing a suitable Grothendieck universe U for this discussion, for those curious. When I say small, I mean U-small. An arbitrary category need not be U-small here, but it will be U'-small for some sufficiently large universe U'.