Kerodon

Some typos: "every map $σ_0:\Lambda^n_i \rightarrow\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ can be extended to an $n$-simplex $σ:\Delta^n \rightarrow \mathcal{C}$."

should be "...can be extended to an $n$-simplex $σ:\Delta^n \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$".

Same issue in the $n=1$ case.

I think in case $n=0$, according to the definitions the horn $\Lambda^0_0$ should be empty and not $\Delta^0$. However, then the condition for $n=0$ reads "there is a 0-simplex in $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$", and I'm not sure if this is wanted (shouldn't we allow the empty groupoid?).

Yep, thanks! Definitely there should be no non-vacuous filling condition in the case n=0.