[[Types of Category]]
# Thin category
A **thin category** is [[locally small category]] where
there is at most one [[morphism]] in every hom-set. #m/def/cat 
That is,
$$
\begin{align*}
(\forall X,Y \in \Ob \cat C)  [\abs{\cat C {(X, Y)}} \leq 1]
\end{align*}
$$
These constitute [[Preorders as categories|preorders-as-categories]].
The additional condition of being a [[Skeletal category]],
makes a [[Posetal category]].

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