Definition:Discrete Category on Set

Definition

Let $S$ be a set.

The discrete category on $S$ is the discrete category $\mathbf{Dis} \left({S}\right)$ with:

Objects:		elements of $S$
Morphisms:		only identity mappings
Composition:		composition of mappings

Also see

• Definition:Graded Object
• Discrete Category on Set is Discrete Category
• Definition:Discrete Category Functor