[Gormisdomai]

"On first reading, it seems magical and deep, but once you grok the proof, it feels like a relatively trivial observation. The whole thing is just about ____ composition!"

I think if you replace _____ with the right word almost every result I've seen in my (albeit somewhat limited) exposure to category theory can be described this way.

(not that that detracts from your answer!)

[eli_gottlieb]

Well yeah, because category theory studies composition. That's what it's for. That's why a category is defined the way it is: a bunch of objects, identity arrows from each to itself, and arrows between them, which enjoy an associative composition operator.