User:Leigh.Samphier/Topology/Isomorphism iff Isomorphism in Dual Cateogry

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Theorem

Let $\mathbf C$ be a metacategory.

Let $\mathbf C^{\operatorname{op}}$ be the dual category of $\mathbf C$.

Let $f$ be a morphism of $\mathbf C$.

Then $f$ is an isomorphism in $\mathbf C$ if and only if $f^{\operatorname{op}}$ is an isomorphism in $\mathbf C^{\operatorname{op}}$.

Proof

$\blacksquare$