# nLab underlying ordinary category

Underlying ordinary categories

# Underlying ordinary categories

## 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.

Created on February 11, 2019 at 23:06:32. See the history of this page for a list of all contributions to it.