Kerodon

Possible typo : " Suppose that the diagram $\sigma$ extends to a functor $\overline{\sigma }: \operatorname{Vert}(G) \rightarrow \operatorname{\mathcal{C}}$ " to " Suppose that the diagram $\sigma$ extends to a functor $\overline{\sigma }: \operatorname{N}_{\bullet }( \operatorname{Vert}(G) ) \rightarrow \operatorname{\mathcal{C}}$ "

Yep. Thanks!

It took me a moment to realise that the notation $\operatorname{N}_{\bullet }( \operatorname{Vert}(G) )$ in (2) was referring to $\operatorname{Vert}(G)$ as a (thin) category using the partial order defined in (1), and not just as a set. Obvious in retrospect, but maybe it could be clarified by saying something like "we can consider $\operatorname{Vert}(G)$ as a partially ordered set" instead of "there is a partial ordering"?