# Discrete category

> A discrete category is a category whose only morphisms are the identity morphisms.

Given a set `𝐴`, we get a discrete category `𝒞`, in which the objects are the elements of `𝐴` and the morphisms are the identity morphisms, one for each `𝑥 ∈ 𝐴`, which are uniquely determined by the identity axiom. A discrete category is so determined by its objects, which correspond exactly to its identity morphisms.