TITLE: What are the prerequisites for learning category theory?
QUESTION [26 upvotes]: 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.

REPLY [12 votes]: 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.