[[Types of Category]]
# Disjoint Category
A **disjoint category** is not a recognised category theoretic term,
but I use it to refer to a category in which every [[morphism]] is an [[endomorphism]]. #m/def/cat
That is,
$$
\begin{align*}
(\forall X, Y \in \cat C) [X \neq Y \implies \cat C {(X, Y)} = \emptyset]
\end{align*}
$$
Such a category may be viewed as the [[coproduct category]] of [[Monoids as categories|monoids-as-categories]].

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#state/tidy | #SemBr | #lang/en