§ Yoneda from string concatenation


I'm trying to build intuition for Yoneda (again) this time from the perspective of strings and concatenation. The idea is that the identity function behaves like the empty string, and "free arrow composition" behaves like string concatenation. So can we understand yoneda from this model?









Now that we understand the "internal" structure, let's imagine we're representing this collection of objects and arrows by some other collection of objects and arrows. So we have a functor F that takes these sets to other sets, and takes these objects to other objects.