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Homotopy Type Theory
dagger 2-poset > history (Rev #4, changes)

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~~## Contents

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~~## Definition

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~~A dagger 2-poset is a dagger category $C$ such that

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- For each object $A:Ob(C)$ and $B:Ob(C)$ and morphism $R:Hom(A, B)$, $S:Hom(A, B)$, a propositional binary relation $R \leq_{A, B} S$
- For each object $A:Ob(C)$ and $B:Ob(C)$ and morphism $R:Hom(A, B)$, $R \leq_{A, B} R$.
- For each object $A:Ob(C)$ and $B:Ob(C)$ and morphism $R:Hom(A, B)$, $S:Hom(A, B)$, $R \leq_{A, B} S$ and $S \leq_{A, B} R$ implies $R = S$.
- For each object $A:Ob(C)$ and $B:Ob(C)$ and morphism $R:Hom(A, B)$, $S:Hom(A, B)$, $T:Hom(A, B)$, $R \leq_{A, B} S$ and $S \leq_{A, B} T$ implies $R \leq_{A, B} T$.
- For each object $A:Ob(C)$ and $B:Ob(C)$ and morphism $R:Hom(A, B)$, $S:Hom(A, B)$, $R \leq_{A, B} S$ implies $R^\dagger \leq_{B, A} S^\dagger$.

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~~## See also

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Revision on June 7, 2022 at 10:54:20 by
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