nLab
empty category

Contents

Definition

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.

Properties

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).

Revised on April 21, 2017 10:52:39 by Urs Schreiber (131.220.184.222)