Category t. book suggestion

1. Feb 15, 2008

matness

I am only familiar to undergrad abstract algebra and want to learn category theory.
which book or website do you suggest for a quick start?

2. Feb 15, 2008

LukeD

So before I give any suggestions, you should know that I probably have less of a background in algebra than you and also haven't yet learned much Category Theory (but I work on it sometimes in my free time).

A while ago, I started a topic where I asked a similar question and did some reading through some books before picking one to start learning from.

The standard text on Category Theory is MacLane's Categories for the Working Mathematician, but it assumes that you're already familiar with a lot of algebra. In particular, I believe that it assumes some knowledge of algebraic topology.

Goldblatt has a book titled Topoi: The Categorical Analysis of Logic. It builds up all of the basic category theory and eventually covers a good deal. It also covers some basic topoi theory. It assumes that you have a fair grasp of undergrad algebra (but it is not necessary that you do).
(Although I don't have a link to Goldblatt's website at this moment, the above link is on his website)
The only problem that I've noticed with the book is that it doesn't seem to have many examples of applications of the earlier ideas. It mainly builds up the basics so that it can get to Topos Theory
That is the book that I am working through at the moment.

3. Feb 16, 2008

masnevets

Why do you want to learn category theory? If you just want to learn it for the sake of learning it, I think it will be tough to digest it without having more background than you mentioned. Despite what some people may think, category theory's purpose is for applications to other math (like algebraic geometry and algebraic topology) and not abstraction for its own sake.

It might be better to start with some homological algebra or algebraic topology so that the stuff you see will be motivated.

4. Feb 16, 2008

matness

Because in algebraic geometry lots of things are explained in terms of categories and functors.Not want deeply learning this stuff but understanding when it is used in definitions thm s etc.

5. Feb 16, 2008

morphism

All the category theory I know (which is not a lot), I learned from chapters I and X of Hungerford's Algebra. It sounds like these two chapters (well, section and a chapter!) will be good enough for you too.

6. Feb 19, 2008

masnevets

In that case, I think the best way to learn category theory is to try and prove some of the things yourself and work out a bunch of examples. I never really understood what a natural transformation was until I was assigned Yoneda's lemma on a problem set. This might not be a bad way to go. In the process I think you would pick up a lot of valuable definitions.