nLab
Pos

Context

Categories of categories

Contents

Definition

PosPos is the category whose objects are posets and whose morphisms are monotone (weakly increasing) maps.

Properties

The hom-sets of PosPos themselves have the structure of posets, making PosPos into a 2-poset (aka (1,2)(1,2)-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 PosPos is the primordial example of a 22-poset.

category: category

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