Bartosz Milewski on Nostr: Exactly! Under the coend, the hom-functor acts like a delta function. I often say ...

Exactly! Under the coend, the hom-functor acts like a delta function. I often say that we can "integrate over the hom-functor." The Australians call it the ninja Yoneda reduction.
∫ˣ𝐶(𝑥,𝑎)×𝐹𝑥≅𝐹𝑎