> I'd say the Yoneda lemma should be in there. It's hard to explain without going through all the definitions but very broadly speaking it gives a precise way t

> I'd say the Yoneda lemma should be in there. It's hard to explain without going through all the definitions but very broadly speaking it gives a precise way to characterize a object by its relations to other objects. To add a bit to that, Yoneda's lemma says that you know everything about an object if you know the ways that it can be mapped to other objects. The "co-Yoneda's lemma", while often less useful in practice (in my practice, anyway), is maybe easier to understand in this intuitive way: you know everything about an object if you know the ways that other objects can be mapped to it, which I have heard phrased as something like "you can learn everything about an object by probing it with other objects."