Remark 21.37.6. Assumptions and notation as in Situation 21.37.1. Note that setting $\mathcal{C}' = \mathcal{D}$ and $u$ equal to the structure functor of $\mathcal{C}$ gives a situation as in Situation 21.37.3. Hence Lemma 21.37.5 tells us we have functors $\pi _!$, $\pi _!^{\textit{Ab}}$, $L\pi _!$, and $L\pi _!^{\textit{Ab}}$ such that $forget \circ \pi _! = \pi _!^{\textit{Ab}} \circ forget$ and $forget \circ L\pi _! = L\pi _!^{\textit{Ab}} \circ forget$.

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