An introduction to algebraic topology from the categorical point of view I'm looking for a modern algebraic topology textbook from a categorical point of view. Basically, I'd like a textbook that uses the language of functors, natural transformations, adjunctions, etc. right from the start.
I'm comfortable with general topology and category theory, but I haven't had much exposure to algebraic topology beyond the basics of the fundamental group(oid) and de Rham cohomology. In particular, I'd like to learn about the various homology and cohomology theories. 

Rotman's An Introduction To Algebraic Topology is a great book that treats the subject from a categorical point of view.  Even just browsing the table of contents makes this clear: Chapter 0 begins with a brief review of categories and functors.  Natural transformations appear in Chapter 9, followed by group and cogroup objects in Chapter 11.
The aspect I like most about this book is that Rotman makes a clear distinction between results that are algebraic and topological.  E.g., he proves several statements about group actions before then applying them to the particular topological setting of covering spaces and the action of the fundamental group on a fiber.
