Category Theory: ???What is up with these Diagrams??? So I found a basic category theory book online and was trying to learn some of the basics. Many of the proofs are done in diagram form (and it seems to very greatly reduce their lengths). However, no where in the book does the author prove that the diagrams make sense, explain exactly how to interpret the diagrams, or say what things like "this diagram commutes" means. I've seen similar treatment of diagrams in category theory in a few books online as well as on websites (such as John Baez's), and I've so far just been entirely lost with them. Could someone point me to somewhere that explains these in at least some semi-rigorous fashion?