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:
- 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
- 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.4.5$