• Interaction With Identities. We have
    \[ \text{id}^{\dagger }_{\mathcal{C}}=\text{id}_{\textup{Hom}_{\mathcal{C}}\webleft (-_{1},-_{2}\webright )}, \]

    i.e. the natural transformation associated to $\text{id}_{\mathcal{C}}$ is the identity natural transformation of the functor $\textup{Hom}_{\mathcal{C}}\webleft (-_{1},-_{2}\webright )$.


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