Definition:Discrete Category

Definition
Let $\CC$ be a metacategory.

Then $\CC$ is said to be discrete it comprises only identity morphisms.

If the collection $\CC$ constitutes the objects of $\mathbf C$, then $\mathbf C$ may also be denoted $\map {\mathbf {Dis} } \CC$.

Also see

 * Definition:One (Category)
 * Definition:Discrete Category on Set