Kerodon

To make the reduction to the case $V$ is an isofibration, it seems that one needs results like "$\mathrm{Fun}(\mathcal{C}/\mathcal{B},\bullet)$ preserves equivalences of $\infty$-categories", which follows by a combination of Proposition 0285 (1), Proposition 0288, and Remark 02TQ (maybe this has been included somewhere I haven't noticed...). Furthermore, at the step one reduces to prove that $\theta$ is a trivial Kan fibration, it will be nice to refer to a relative version of Remark 02TQ (consider a functor $\mathcal{D}\to\mathcal{E}$ in place of $\mathcal{D}\to\Delta^0$).

Little typos: In the proof, under the definition of $\bar{G}$, there is a double "denote"; and in the choice of $G_0$, $\mathcal{K}^{\triangleright}$ should be corrected as $\mathcal{K}$.

Yep. Thanks!

Little typo missed: In the last second sentence of the proof, it seems that $G$ should be a $V$-left Kan extension rather than a left Kan extension.

Yep. Thanks!