9
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ Write it. You'll be the first! $\endgroup$ – Will Jagy Jul 13 '14 at 3:04
  • 5
    $\begingroup$ One of the problems with "lots of examples" in category theory is that it is often useful to have a lot of knowledge, first - algebra, topology, some set theory, posets, etc. Not saying that there isn't such an approach, but the best category theory book depends on what you know already. For example, is a category theory book that talks about homology much use? $\endgroup$ – Thomas Andrews Jul 13 '14 at 3:06
  • 4
    $\begingroup$ I attempt to understand category theory at least once a year. $\endgroup$ – copper.hat Jul 13 '14 at 3:27
  • 1
    $\begingroup$ Awodey's book is rather good at that. The examples are mostly done through partially ordered sets and the lambda-calculus. I personally have found it useful to look through nLab for more examples (where they exist), but Thomas Andrews is right: knowing a bunch of knowledge of algebra, topology, and set theory is useful for examples. Awodey attempts to present the examples involving partial orders and lambda calculus without assuming prior knowledge, but it still might be useful for the intuition. $\endgroup$ – Hayden Jul 13 '14 at 3:32
  • 2
    $\begingroup$ Handbook of Categorical Algebra: Volume 1,2,3 Basic Category Theory- Francis Borceux Cambridge University Press $\endgroup$ – Babai Jul 13 '14 at 11:58
3
$\begingroup$
  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.

  2. 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.)

  3. 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.

$\endgroup$
  • 1
    $\begingroup$ Yeah, The Joy of Cats = The Joy of Examples. $\endgroup$ – Fizz Apr 12 '15 at 14:57
3
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Thanks, I already own this one, it is really good. $\endgroup$ – Jorge Fernández Hidalgo Apr 12 '15 at 15:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.