Kerodon

It's probably not worth mentioning, but in the third bullet you write "Let $U \colon \mathcal{C} \to \mathcal{D}$ be a Cartesian fibration of simplicial sets and let $f \colon K \to \mathcal{C}$ be any morphism of simplicial sets.", where everywhere else cartesian fibration is written uncapitalized.

Yep. Thanks! That's going to be a tough habit to break.

In the introduction you one time write a condition for $g$ being cocartesian and then write a condition for $g$ being cartesian that you claim to be an equivalent reformulation in terms of nerves of categories. I suppose the first conidition is already the condition for $g$ being cartesian.

Also: There is one more occasion where it is written "Cartesian fibration" instead of "cartesian fibration" at the last bullet when properties of cartesian fibrations are explained.

At the same spot: "... which we prove in §5.4.5).": the ')' is superfluous.

Yep. Thanks!

In the third paragraph, "For every object $W \in \operatorname{\mathcal{E}}$ having image $\overline{X} = U(X) \in \operatorname{\mathcal{C}}$...", the $X$ should be $W$.

Yep. Thanks!