# What are the prerequisites for learning category theory?

Is category theory worth learning for the sake of learning it? Can it be used in applied mathematics/probability? I am currently perusing Categories for the Working Mathematician by Mac Lane.

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Pet peeve: it's Mac Lane, with a space and capital letters in both parts. –  Arturo Magidin Nov 2 '10 at 3:46
I guess I wrote his original name. –  PEV Nov 2 '10 at 3:50
Not quite: the original name lacked the space, but not the capital L. (-; –  Arturo Magidin Nov 2 '10 at 3:53

It depends on whether you are talking about Category Theory as a topic in mathematics (on a par with Geometry or Probability) or Category Theory as a viewpoint on mathematics as a whole.

If the former, the main prerequisite is that you should have encountered a situation where you wanted to move from one type of "thing" to another type of "thing": say from a group to its group ring, or from a space to its ring of functions, or from a manifold to its differential graded algebra.

If the latter, then there are no prerequisites and it is a Very Good thing to do! But if the latter, then reading Mac Lane isn't necessarily the best way to go. However, I'm not sure if there is a textbook (or other) that tries to teach elementary mathematics (of any flavour) from a categorical viewpoint. I try to teach this way, but I've not written a textbook! I wrote a bit more on this in response to a question on MO, I copied my answer here.

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Well, there's Linderholm's Mathematics Made Difficult, which treats elementary arithmetic from a categorical viewpoint -- with tongue firmly embedded in cheek... –  Rahul Nov 2 '10 at 13:14
Peter May's "Concise Course in Algebraic Topology" would be an excellent way to learn some category theory while learning other stuff. –  Ryan Budney Nov 2 '10 at 14:34
@Ryan, @Rahul: Great! Didn't know of the first, and didn't know that the second was so categorical. I'll add them to my list of books to take a look at. –  Loop Space Nov 2 '10 at 20:36