I'm an economist/statistician/game theorist, but I'm not a mathematician. I wanted to learn Category Theory, but being that I'm not in an academic setting and this isn't something economists usually do, I was on my own with the textbooks. This repository holds two documents.
One is my notes, an attempt to explain Category Theory to myself, compiled to a PDF at https://raw.githubusercontent.com/b-k/cat_notes/master/cat_notes.pdf . Some would be very obvious to a mathematician, but are sufficiently outside my usual way of thinking that I felt them worth clarifying to myself, and writing down to verify I understand them clearly. I made them public because maybe, if you're also somebody who knows a relatively good amount of math but is not a mathematician, they may be useful to you too.
Math is extremely vocabulary-heavy. Every statement, every theorem, is of the form define a thing, then define another thing; these things are related via a relationship we have defined. You could conceivably read a book in a language you don't speak by looking up every word, but if you hope to make any progress in reasonable time you will need to know the basic vocabulary without thinking too much about it. So, much of the content in this repository is in the form of flash cards. There are some theorems and simple exercises, but keeping to the spirit of mathematics, the great majority of cards cover definitions.
This repository, then, includes a document of general conceptual notes to myself, in
cat_notes.tex, and a much longer set of flash cards, in cat_cards.tex.
License: CC-BY-NC-SA.
Everything is in LaTeX. If you have the (updated rewrite) XeLaTeX installed, run
make doc to compile. Run make cards to generate the card set.
The commutative diagrams essential to Category Theory use tikz-cd. You'll have to
have the appropriate tikz packages installed, and the additional tikz-related files
in this repository should get you the rest of the way. The python script calls pdfjam
and pdfcrop, which may already be part of your LaTeX installation.
Generate the flash cards via make cards, which runs a python script (a hack that
is all but a shell script) to generate a randomized set of cards, one front on a page
followed by one back on the next. This is the format you want for going through flash
cards on your telephone. If you'd like to actually print them, change onecard at the
top of cat_cards.tex to one of the standard formats in the flash cards package like
avery5371.