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 $n$-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)