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Question about the proof of Kerodon tag 030V (Proposition 7.3.7.1)

$\require{AMScd}$ Related to this, I have a question about the proof given in Kerodon of the following result: Proposition 7.3.7.1: Let $C$ be an $\infty$-category, let $\bar{F} : C^\rhd \to D$ be a ...
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