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 ti

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/