Exercises in category theory for a non-working mathematican (undergrad)

I'm trying to learn category theory pretty much on my own (with some help from a professor). My main information source is the good old Categories for the working mathematician by Mac Lane. I find the book very good and and I don't have very much trouble understanding the theory, proofs and motivations and so on.

But many examples fly over my head as do the exercises.

The thing is that I'm far from a working mathematician or a grad student, which the book seems to be aimed towards. I know that one have to do learn math by doing math and I find it almost impossible when exercises involve things I'm not yet familiar with (modules, algebras etc). I simply don't have time to learn these things just so I can solve my exercises but on the other hand I don't want to miss out on learning things just because the exercises are on a too high level for me.

So I want to ask you for references on exercises in category theory aimed at someone with limited knowledge of abstract algebra, suitable for concepts in Categories for the working mathematician but with more basic objects but still meaningful and challenging.

(I consider myself to have fairly good basic knowledge of "elementary"-style abstract algebra (monoids, groups, rings, fields, linear algebra, some galois theory, related number theory, some algebraic graph theory etc))

Check out the new book (amazon-link)

Tom Leinster, Basic Category Theory, Cambridge Studies in Advanced Mathematics, Vol. 143, 2014

A more elementary text is Conceptual Mathematics: A First Introduction to Categories. Also interesting is the list given here.