nLab
ASSet

Definition

The category ${\mathrm{sSet}}_{+}$ of augmented simplicial sets is the category of presheaves on the augmented version of the simplex category ${\Delta }_a$:

$${\mathrm{sSet}}_{+}:={\mathrm{Set}}^{{\Delta }_a^{\mathrm{op}}}.$$sSet_+ := Set^{\Delta^{op}_a} \,.

This is the category whose objects are augmented simplicial sets and whose morphisms are the evident morphisms between these.

Related concepts

• sSet

• asSet

Applications

The join of simplicial sets is most naturally defined via a construction on augmented simplicial sets.

category: category