References: Introductory Books for Algebraic Topology

Question

I'm looking for books that teach algebraic topology, which use (and construct the machinery as well) categories and homological algebra from its beginning. What would be good books for that?

Answer 1

Try book Introduction to Topological Manifolds by Jhn M Lee...Here is the link. Its much easier to understand than Hatcher. http://www.springer.com/in/book/9781441979391c

Answer 2

I've been looking for a good algebraic topology book for a while, and I still haven't found one that's right for me. Category theory is a subject I find extremely fun, and given how important it is to algebraic topology, that makes hard for me to be comfortable diving deep into a textbook that eschews that machinery.

I've found the best options are the following three, although I'm not gungho about any:

• The book by tom Dieck assumes you know basic category theory, but it's extremely dense. I've found it very hard to learn new material from, but it's closer to what you're asking for than any others I know of. It's definitely possible that someone with more mathematical talent would love it, I just have had a very hard time with it personally.

• Rotman incorporates a little bit of the machinery early on at least, so you might want to try that one. He has a different book specifically on homological algebra that I think is very good overall, but I found the algebraic topology text much more dry.

• May's "Concise Course" was way too concise for me, but like tom Dieck, could be great for someone with better mathematical ability.