• Characterisations. The following conditions are equivalent:
    1. The functor $F$ is conservative.
    2. For each $f\in \textup{Mor}\webleft (\mathcal{C}\webright )$, the morphism $F\webleft (f\webright )$ is an isomorphism in $\mathcal{D}$ iff $f$ is an isomorphism in $\mathcal{C}$.

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