Category Theory textbook (learning through guided discovery Dummit and Foote)
sorry for asking the same question in a slightly different angle, I want a book in Category Theory similar to Dummit and Foote's book in Abstract Algebra. I want it to have tons of examples and problems, and I want it to be the sort of book in which you always have an idea about what the next results are going to be. Something I really liked about Dummit and Foote is I understood what was going on the first time I read it, but when I read it a second time I felt a lot better than the first time (I'm looking forward to a third).
Sorry if this just sounds like a lost of demands, I just wanted to give some information about what I was looking for.
Thank you kindly
Regards.
Solution 1:
Conceptual Mathematics: A First Introduction to Categories - F. William Lawvere, Stephen H. Schanuel. This was recommended by John Baez on his site as a good introduction to Topos Theory.
Abstract and Concrete Categories: The Joy of Cats (Dover Books on Mathematics) - Jiri Adamek, Horst Herrlich, George E Strecker. This one has tons of examples and is cheap. (Free if you don't need a hardcopy, the authors have a pdf on their site.)
Algebra: Chapter 0 introduces Categories in the first chapter and uses the language of category theory to introduce modern algebra. This one should go very well alongside D&F. The problem with this as an algebra text is that it doesn't have to much on Galois theory, whereas D&F has tons. They should complement each other nicely.
Solution 2:
Add to the above an undergraduate textbook which doesn't have categor[y/ies] in its title, but nevertheless is mostly about motivating category theory with plenty of examples (and then illuminates them with CT):
George M. Bergman An Invitation to General Algebra and Universal Constructions.
There's a 2nd ed. of his book out, so I'm guessing the book was reasonably popular. There's also a free edition on the author's site.