nLab underlying ordinary category

Definition

Let $(V,\otimes,I)$ be a monoidal category and $C$ a $V$-enriched category. The underlying ordinary category of $C$ is the ordinary category $C_0$ with the same objects and with hom-sets

$$C_0(x,y) = V(I,C(x,y)).$$

This is an instance of change of enriching category.