• Interaction With Natural Isomorphisms. The following conditions are equivalent:
    1. The natural transformation $F^{\dagger }\colon \textup{Hom}_{\mathcal{C}}\Longrightarrow {\textup{Hom}_{\mathcal{D}}}\circ {\webleft (F^{\mathsf{op}}\times F\webright )}$ associated to $F$ is a natural isomorphism.
    2. The functor $F$ is fully faithful.

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