[[Types of Category]]
# Discrete category
A **discrete category** is a category in which the only morphisms are identity morphisms. #m/def/cat
$$
\begin{align*}
(\forall X \in \Ob \cat C) [\cat C {(X, X)} = \{\id_X\}] \\
(\forall X, Y \in \cat C ) [X \neq Y \implies \cat C {(X, Y)} = \emptyset]
\end{align*}
$$
Any [[Class]] of objects may be viewed as a discrete category. The
[[Trivial category]], the [[Initial and terminal objects|Initial Object]] in [[Category of small categories]], is itself a discrete category.

It is itself a [[Disjoint category]], [[Groupoid]], and [[Posetal category]].

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#state/tidy | #SemBr