nLab
thin category

Thin categories

Definition

A thin category is a category in which, given any two objects xx and yy and any two morphisms ff and gg from xx to yy, the morphisms ff and gg are equal:

the basic property of thin categories

Up to isomorphism, a thin category is the same thing as a proset. Up to equivalence, a thin category is the same thing as a poset. So mostly we just talk about posets here, but some references want to distinguish these from thin categories. (It is really a question of whether you're working with strict categories, which are classified up to isomorphism, or categories as such, which are classified up to equivalence.)

Examples

Since a poset is a thin category, in particular (semi)lattices, Heyting algebras, frames are, too.

Revised on November 28, 2012 15:05:39 by Urs Schreiber (82.169.65.155)