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I should have mentioned in my post that I have an applied math masters and a solid amount of analysis and linear algebra with some group theory, set theory, and

I should have mentioned in my post that I have an applied math masters and a solid amount of analysis and linear algebra with some group theory, set theory, and a smattering of topology (although no algebraic topology). So, I'm not coming to this with nothing, although I don't have the very deep well of abstract algebra training that a pure mathematician coming to category theory would have. Although, it feels like category theory _ought_ to be approachable without all those years of advanced training in those other areas of math. Set theory is, up to a point. But maybe that isn't true and you're restricted to trivial examples unless you know groups and rings and fields etc.?

griffzhowl 1y ago
You could take a look at Topology: A Categorical Approach by Bradley, Bryson and Terilla. It's a crisp, slim book, presenting topology categorically (so the title is appropriate). It both deepens the undergraduate-level understanding of topology and serves as an extended example of how category theory is actually used to clarify the conceptual structure of a mathematical field, so it's a way to see how the flesh is put on the bare bones of the categorical concepts. It's also available for free online: https://topology.mitpress.mit.edu/ https://topology.mitpress.mit.edu/
- griffzhowl 1y ago
  Actually this is a better source for it because it includes a pdf of the table of contents and links to supplementary videos https://jterilla.github.io/TopologyBook/ https://jterilla.github.io/TopologyBook/