To be clear, how much category theory are you envisioning setting up in a first course on abstract algebra? Are you basically just talking about a modern treatm

To be clear, how much category theory are you envisioning setting up in a first course on abstract algebra? Are you basically just talking about a modern treatment of morphisms in the abstract sense, or do you also mean discussing things like functors? My perspective on this is basically informed by the following: I like category theory a lot. I've chatted with Baez about this on a few occasions and insofar as I need to use algebra, I like the category theoretic formalisms that come along with it. I think if you had students with a lot of mathematical maturity but no prior exposure to abstract algebra (except maybe a rigorous treatment of linear algebra), you could accomplish what you're proposing. To your point, one of my favorite math textbooks is Aluffi's Chapter 0. You're probably familiar with it, but if not: it builds up abstract algebra in a rigorous and modern fashion alongside category theory. However, there are a few caveats here: 1. Aluffi explicitly states it's a textbook for upper level undergrads and preferably graduates. In my experience, when authors say this they actually mean it's appropriate as a year one graduate course. That's not the time to learn abstract algebra for the first time! 2. Aluffi does a great job of covering things like morphisms and categories, but the size of the book is massive. He doesn't have any nontrivial coverage of deeper category theoretic concepts like functors until much later in the book; it's probably far enough in that you couldn't reasonably cover it in a single semester course. 3. I really don't think most math majors would benefit from it. Those who are applied math majors will get questionable benefit from a slower, more comprehensive approach to algebra than a faster approach that lets them get to applications. Moreover, not all pure math majors have the mathematical maturity to approach category theory before grad school. Proofs in traditional abstract algebra are a lot less abstract than category theory, and it's easier to motivate them even if they aren't ultimately as elegant.