An Introduction to Homological Algebra

This is a bit of an odd suggestion, but I learned the basics of category theory from the appendix to Weibel’s “An Introduction to Homological Algebra”. I’m not sure why, but I think the fact that it’s an appendix meant the author had no motivation to inflate the content unnecessarily. So it’s more like a pamphlet; only about 30 pages IIRC, and it’s really just the bare-bones definitions and facts. The full-on textbooks dedicated to category theory have way too much superfluous content IMO, unless your aim is to be a researcher in that field specifically.