# nLab category of V-enriched categories

### Context

#### Enriched category theory

enriched category theory

# Contents

## Idea

For $\mathcal{V}$ a suitable context of enrichment (notbaly: for $\mathcal{V}$ a cosmos) there is a $2$-category $\mathcal{V} Cat$ whose

Sometimes one also considers $\mathcal{V} Cat$ as a mere category by dropping the $2$-morphisms (and using enriched strict categories).

## Examples

• For $\mathcal{V} = ($Set$, \times)$, $\mathcal{V}Cat \simeq$ Cat, the $2$-category of locally small categories.

• For $\mathcal{V} = ($Cat$, \times)$, $\mathcal{V}Cat \simeq$ Str2Cat, the $2$-category of strict 2-categories.

$(n+1,r+1)$-categories of (n,r)-categories

category: category

Revised on October 31, 2012 01:57:48 by Toby Bartels (64.89.53.173)