Hello

Well, maybe one should not advertise oneself but a long time ago I  
wrote a chapter on "Basic Category Theory" in the Handbook of Logic in  
Computer Science" (Eds. S. Abramsky, D.Gabbay, T.S.E. Maibaum). Basic  
notions of category theory (and somewhat more) are introduced from the  
viewpoint of functional programming (and other applications in  
computer science).
Maybe a bit outdated if you consider developments in linear logic,  
coalbras, and applications of categories in particular in physics (http://categorieslogicphysics.wikidot.com/video 
), but the chapter still may help to understand some of the basic  
concepts from a programmers point of view (for adjunctions some  
familiarity with automata theory is assumed, though - in former times  
standard knowledge in CS).

Regards

Axel

PS. Mildly ignore the mistakes.