A Gentle Introduction to Category Theory [pdf]

Not just FP researchers, although they are a particularly good fit because typed lambda calculi are Cartesian closed categories.

Other areas of CS where category theory is applied:

1. Algebraic data types and modules. E.g., http://reperiendi.wordpress.com/2007/11/03/category-theory-f...

2. Semantics of non-terminating programs. E.g., http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.2...

3. Semantics of concurrency. E.g., http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.62.8...

These are probably the most important places, besides FP, where categories are used in computer science, but there are others: logic programming, computer graphics and vision, knowledge representation, ontology, &c. The applications to FP are most visible because (i) Haskell monads are a little slice of category theory, so users as well as language designers need to get their hands dirty[+], and (ii) it's very natural to want a realisation of a categorical semantics to have first-class functions, ideally lazy functions, because that makes the realisation easier.

[+] Categorical abstractions in semantics are dirty, don't let people fool you into believing they are pure and clean.

So one should introduce category theory along with its usage. Category theory makes little sense without it -- it turns to mundane symbol (or rather, diagram) manipulation. The category-theoretical notions do not seem to have any relevance if you do not know what other notions they try to generalize. What I mean is that it is more natural to notice that various products in all kind of mathematical structures have some universal property in common, than to say that these are examples of categorical notion of product. Or, it is more natural to notice that van Kampen's theorem really says something about connection between fundamental groups of a space and its subspaces, than to say that fundamental grupoid of a space is a colimit of a diagram created by fundamental grupoids of certain families of subspaces, with arrows being induced by inclusions. The second approach in case of van Kampen theorem (and many more, actually) is useful when you want to prove or use van Kampen theorem, because it is a bit easier to prove an universal property of a colimit than to prove that the fundamental group of a space is a free product product of the fundamental group of its subspaces with an amalgamation along fundamental group of their intersection. Nevertheless, categorical approach does not provide you with the intuition which initially led to the formulation of this theorem. I believe that the case is similar with your friend's work -- it's his intuition and insight which led him to notice this equivalence, and category theory only helps him formulate his thoughts in an elegant way.

Learning category theory before learning more substantial facts is in my opinion going totally in backward order. Or maybe I'm just an (metaphorically) old grump and refuse to acknowledge the revolution just like mathematicians in the beginning of twentieth century were refusing to accept set theory.

For a demonstration,

I recommend the "Going Deep" show episodes of Erik Meijer and Brian Beckman, http://channel9.msdn.com/search?term=erik+meijer+brian+beckm...

plus the book "Algebra of Programming" by Richard Bird, Oege de Moor http://www.amazon.com/Algebra-Programming-Prentice-Hall-Inte...

Functor pattern is certainly something else than functor in category theory.

By "useful" I mean "useful in getting new results or new, better proofs". By this metric, singular homology is certainly useful, because it enables us to create clean and elegant proofs of some highly non-trivial and interesting facts, but I cannot imagine anything more useless in real life.