> 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!