nLab
empty category

The empty category is the category with no objects (and hence no morphisms). It is a groupoid, so we may call it the empty groupoid. One can similarly speak of the empty nn-category, the empty \infty-groupoid, etc etc etc.

The empty category is discrete, hence may be identified with a set: the empty set. This set is a subsingleton, so we may also identify it with a truth value: the false one.

The empty category is initial in Cat (as well as Grpd, ∞Grpd, Set, etc).

Created on August 27, 2010 02:43:36 by Toby Bartels (75.88.93.39)