# Notation: why are categories enriched over $\mathcal V$?

In most references about enriched categories, $$(\mathcal V, \otimes)$$ is supposed to be a monoidal category and then $$\mathcal V$$-enriched categories are defined.

Why is the letter $$\mathcal V$$ used for a monoidal category?

• I'm not sure, but one of the basic examples of a monoidal category is $\mathcal{V}= k-\mathbf{Vect}$ for some field $k$ : the $V$ would then be here for "vector" or "vector space" – Max Feb 9 at 13:20
• Perhaps originating from a term like virtual sets (just a guess). – Berci Feb 10 at 12:38