nLab
ASSet

The category of augmented simplicial sets is the category of presheaves on the augmented version of the simplex category ${\Delta }_a$ (the full subcategory of Cat on finite but possibly empty linear quivers):

$$\mathrm{ASSet}:={\mathrm{Set}}^{{\Delta }_a^{\mathrm{op}}}.$$ASSet := Set^{\Delta^{op}_a} \,.

Compare with the category SimpSet of ordinary simplicial sets.

An application is the definition of the join of simplicial sets.

category: category