Definition:Three (Category)

Definition
The category $\mathbf 3$, three, is the category:


 * $\begin{xy}

<0em,0em>*+{*} = "x", <5em,0em>*+{\star} = "y", <5em,-5em>*+{\bullet} = "z",

"x";"y" **@{-} ?>*@{>}, "y";"z" **@{-} ?>*@{>}, "x";"z" **@{-} ?>*@{>} \end{xy}$

with:


 * Three objects, $*$, $\star$ and $\bullet$; and
 * Six morphisms:


 * The three identity morphisms $\operatorname{id}_*$, $\operatorname{id}_\star$, $\operatorname{id}_\bullet$;
 * One non-identity morphism $* \to \star$;
 * One non-identity morphism $\star \to \bullet$;
 * One non-identity morphism $* \to \bullet$.