I second this recommendation; Cheng's book is probably the most approachable of the recent wave of category theory texts which does not assume the whole edifice of abstract algebra as a starting point.
Most CT texts introduce categories around page 1, and the Yoneda lemma a handful of pages in. Cheng's book builds up intuitions until chapter 8, where categories are defined over the course of several pages, and supposedly (I'm not there yet) ends the book with the Yoneda lemma.
You might think this means the book is mostly fluff. First: if you read it and think that, you're probably a more advanced reader than she's targeting. Second: goodness no, it's packed to the brim with categorical intuitions; there's a whole way of thinking that she's trying to motivate. Categories are just a formalization of this way of thinking; if you're not onboard with the thinking, the formalization is going to be hollow to you no matter what.
Most CT texts introduce categories around page 1, and the Yoneda lemma a handful of pages in. Cheng's book builds up intuitions until chapter 8, where categories are defined over the course of several pages, and supposedly (I'm not there yet) ends the book with the Yoneda lemma.
You might think this means the book is mostly fluff. First: if you read it and think that, you're probably a more advanced reader than she's targeting. Second: goodness no, it's packed to the brim with categorical intuitions; there's a whole way of thinking that she's trying to motivate. Categories are just a formalization of this way of thinking; if you're not onboard with the thinking, the formalization is going to be hollow to you no matter what.
Do recommend.