[griffzhowl]

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/

[griffzhowl]

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/