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Remark 18.19.6. In the situation of Lemma 18.19.2 the diagram

\[ \xymatrix{ \textit{Mod}(\mathcal{O}_ U) \ar[r]_{j_{U!}} \ar[d]_{forget} & \textit{Mod}(\mathcal{O}_\mathcal {C}) \ar[d]^{forget} \\ \textit{Ab}(\mathcal{C}/U) \ar[r]^{j^{Ab}_{U!}} & \textit{Ab}(\mathcal{C}) } \]

commutes. This is clear from the explicit description of the functor $j_{U!}$ in the lemma.

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