Pos

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

The hom-sets of $Pos$ themselves have the structure of posets, making $Pos$ into a 2-poset (aka $(1,2)$-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 $Pos$ 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)