> By the way, when you have a \$$\mathcal{V}\$$-enriched category \$$\mathcal{Z}\$$ and two objects \$$a\$$ and \$$b\$$ in it, we call \$$\mathcal{Z}(a,b) \in \mathcal{V}\$$ the **hom-object** from \$$a\$$ to \$$b\$$. This is like when we have an ordinary category \$$\mathcal{Z}\$$: then \$$\mathcal{Z}(a,b)\$$ is a set, called the **hom-set** from \$$a\$$ to \$$b\$$ and often written \$$\text{hom}(a,b)\$$. In the enriched case \$$\mathcal{Z}(a,b) \in \mathcal{V}\$$ is not analogous to a morphism; it's analogous to a set of morphisms.

Okay, that makes sense. Thanks for the clarification!