Definition:Three (Category)

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Definition

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

$\begin{xy} <0em,0em>*+{\circledast} = "x", <5em,0em>*+{\star} = "y", <5em,-5em>*+{\bullet} = "z", "x";"y" **@{-} ?>*@{>}, "y";"z" **@{-} ?>*@{>}, "x";"z" **@{-} ?>*@{>} \end{xy}$

with:

Three objects, $\circledast$, $\star$ and $\bullet$; and
Six morphisms:
  • The three identity morphisms $\operatorname{id}_\circledast$, $\operatorname{id}_\star$, $\operatorname{id}_\bullet$;
  • One non-identity morphism $\circledast \to \star$;
  • One non-identity morphism $\star \to \bullet$;
  • One non-identity morphism $\circledast \to \bullet$.


Also see


Sources