Skew Monoidales in $Span$

Abstract

This article consists of an interesting characterisation of a skew monoidale in the monoidal bicategory $Span$. After discussing the shift or decalage functor on simplicial sets we characterise these skew monoidales as categories $\mathbb C$ together with a functor $R \colon Dec(\mathbb C) \longrightarrow \mathbb C$ which satisfies two conditions and give an example where the unit of the skew monoidale is not of a restricted type.