# nLab Pos

### Context

#### Categories of categories

$\left(n+1,r+1\right)$-categories of (n,r)-categories

# Contents

## Definition

$\mathrm{Pos}$ is the category whose objects are posets and whose morphisms are monotone (weakly increasing) maps.

## Properties

The hom-sets of $\mathrm{Pos}$ themselves have the structure of posets, making $\mathrm{Pos}$ into a 2-poset (aka $\left(1,2\right)$-category) or locally posetal 2-category. If Set is the primordial example of a category and Cat is the primordial example of a 2-category, then $\mathrm{Pos}$ is the primordial example of a $2$-poset.

category: category

Revised on October 30, 2012 19:59:59 by Urs Schreiber (131.174.189.66)