nLab empty simplicial set

Definition

The empty simplicial set is the simplicial set $\varnothing_\bullet$ all whose component sets are empty sets:

$$\underset{n \in \mathbb{N}}{\forall} \;\; \varnothing_n \;=\; \varnothing.$$

The face- and degeneracy maps are, accordingly, each the unique empty function from the empty set to itself.

Properties

• The empty simplicial set is a strict initial object in the category of SimplicialSets.

Related concepts

• empty set, empty subset

• empty type, empty context

• empty family, empty function, empty bundle

• empty topological space, empty simplicial set

• empty graph, empty category, empty diagram

• nothing