Speaking of applying category theory to computational complexity, I've been thinking of NP-complete problems as terminal objects in the category of problems in NP with arrows \\(a \to b\\) when \\(a\\) can be reduced to \\(b\\). I'm sure that's a trivial observation, but it was surprisingly handy when I was helping a friend understand how NP-completeness is special and why NP-hardness is something we'd ever think to consider.