nLab
empty simplicial set

Contents

Definition

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

n n=. \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