I'm about to finish Aluffi's "algebra: chapter 0" and am a bit confused as to what should be my next move. I've been planning to read Tom Dieck's Algebraic Topology for some time now. I glimpsed at it several times and the style of writing very much matches my own taste.
The thing is, although I have some grasp of categories from Aluffi, my grounding in category theory isn't as solid as I would like. And since the book by Dieck uses categories extensively I'd like to be a bit more fluent in the language before approaching it.
Towards this purpose (and since i'm interested in both homological and commutative algebra regardless) I had the idea of finding a book that starts with a formal treatment of the basics of category theory and moves to more advanced/specialized concepts in a moderate pace. That way i could start reading until i'm completely comfortable with the language, then pick up Dieck's "algebraic topology" and read the two books simultaneously. After surfing the web a bit i found the following title.
It looks like the book for me. The problem is i didn't find any reviews about it so i'm not so sure.
Can anyone recommend a book that could fill the roles i described?
Might be relevant that I prefer to read books cover to cover than to pick up different things from different sources.
My background (rough description):
- Differential geometry (Guilliam and Pollack + in the middle of Jefferey lee's book)
- Algebra (Aluffi + Herstein).
- Topology (Munkres)
- Analysis (baby+big Rudin, currently reading "Functional Analysis" by Rudin)