Solid applications of category theory in TCS?

I've been learning a few bits of category theory. It certainly is a different way of looking at things. (Very rough summary for those who haven't seen it: category theory gives ways of expressing all kinds of mathematical behavior solely in terms of functional relationships between objects. For example, things like the Cartesian product of two sets are defined completely in terms of how other functions behave with it, not in terms of what elements are members of the set.) I have some vague understanding that category theory is useful on the programming languages/logic (the "Theory B") side, and am wondering how much algorithms and complexity ("Theory A") could benefit. It might help me get off the ground though, if I know some solid applications of category theory in Theory B. (I am already implicitly assuming there are no applications in Theory A found so far, but if you have some of those, that's even better for me!) By "solid application", I mean: (1) The application depends so strongly on category theory that it's very difficult to achieve without using the machinery. (2) The application invokes at least one non-trivial theorem of category theory (e.g. Yoneda's lemma). It could well be that (1) implies (2), but I want to make sure these are "real" applications. While I do have some "Theory B" background, it's been a while, so any de-jargonizing would be much appreciated. (Depending on what kind of answers I get, I might turn this question into community wiki later. But I really want good applications with good explanations, so it seems a shame not to reward the answerer(s) with something.)