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The Yoneda lemma is the obvious answer I think
It’s a precise way to say “anything is perfectly determined by its relationship to everything else”
Can you say why that's interesting?
It gives you a more concrete way to think about categories, just like Cayley's theorem https://en.wikipedia.org/wiki/Cayley%27s_theorem … (which is a special case of the Yoneda lemma) lets you think of any finite group as a bunch of permutation matrices.
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