Definition 8.5.5.1.1 (013E): Essentially Injective Functors

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A functor $F\colon \mathcal{C}\to \mathcal{D}$ is essentially injective if it satisfies the following condition:

For each $A,B\in \text{Obj}\webleft (\mathcal{C}\webright )$, if $F\webleft (A\webright )\cong F\webleft (B\webright )$, then $A\cong B$.

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