Lemma 58.4.5. In diagram (58.4.0.1) the following are equivalent

the image of $h'$ is normal, and

for every connected object $X'$ of $\mathcal{C}'$ such that there is a morphism from the final object of $\mathcal{C}''$ to $H'(X')$ we have that $H'(X')$ is isomorphic to a finite coproduct of final objects.

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