My two resources for learning category theory are the book by Steve Awodey and a series of youtube videos by Bartosz Milewski.
I draw and write a lot of stuff on paper, but clearly things are more portable if put into a svg.
Learning the definitions by heart is a sound strategy in mathematics, because you have to know them sooner or later anyway. Later you "know" and "feel" them, but for starters you can just learn them like words in a foreign language.
