# nLab umbrella category

category theory

## Applications

###### Definition

An umbrella category is an inhabited category $C$ such that for every object $X$ in $C$, there is at least one subterminal object $T$ such that the hom-set $C(X,T)$ is inhabited (hence being a singleton).

Created on June 26, 2011 15:54:57 by Urs Schreiber (89.204.153.100)