Kerodon

The horn inclusion in the final diagram is invisible.

Yep. Thanks!

In the fourth sentence of the proof, "denote the image fo" should read "denote the image of"

Also, the final sentence of the proof seems to be incomplete. Probably it should say something like "It follows that the lifting problem [diagram] admits a solution which...".

Yep. Thanks!

Typo: After the depicted 2-simplex in the proof, “$\underline{e}: \underline{y} \rightarrow \underline{y}'$” should read “$\underline{e}: \underline{y} \rightarrow \underline{z}$”.

"Let $e: \underline{y} \to \underline{y'}$ denote the image of $e$" seems to be "Let $e: \underline{y} \to \underline{z}$ denote the image of $e$"

Yep. Thanks!

In condition (2) the statement "there exists a vertex y∈Y" should be removed, as y is already fixed as the basepoint of Y.