Abstract
We develop the Yoneda perspective: the Yoneda embedding y: C → [C^op, Set] is fully faithful for any locally small category C. The corollary X ≅ Y ↔ Hom(−,X) ≅ Hom(−,Y) supplies a precise sense in which an object is its system of relationships—the natural number 58 is the representable functor Hom(−,58). We give the full proof of the Yoneda lemma, exhibit the density theorem, and link Yoneda to univalence: the equivalence Hom(−,X) ≅ Hom(−,Y) ⇒ X = Y is internalized as a path in the universe.