[suddensleep]

Plug for a friend's book that is forthcoming later this summer, "Topology: A Categorical Approach". [1]

I can't speak to its contents per se, because there isn't a preview yet, but I can speak to the quality of exposition in the lead author's math blog. [2]

I haven't ever dug too much into category theory for its own sake (usually just one-off chapters or appendices that get included in books on other topics), but my understanding is that it unites a lot of mathematical topics. As such, this book might be of more interest to you than, say, a classical point-set topology text, given your desire to uncover connections. That being said, there may be other category-theory-flavored books on other more strictly algebraic topics that would suit your fancy more.

[1] https://mitpress.mit.edu/books/topology

[2] https://www.math3ma.com/

[eindiran]

If you have a CS background and are looking to dig in to category theory a bit more, I would recommend checking out Benjamin Pierce's Basic Category Theory for Computer Scientists. It's a nice, concise introduction to the topic that examines a few very interesting applications to CS.

https://www.goodreads.com/book/show/1810837.Basic_Category_T...

[davehcker]

Right! I have still not finished it, but it's truly enchanting and exactly as you mentioned.