On complicial homotopy monoids

TL;DR

This paper introduces a new class of monoids generalizing simplicial homotopy groups for weak complicial sets, extending homotopy theory in higher categories.

Contribution

It constructs monoids that generalize simplicial homotopy groups for weak complicial sets, broadening the scope of homotopy invariants.

Findings

Constructed monoids for weak complicial sets with a vertex.

Generalized simplicial homotopy groups to a broader setting.

Provided a new algebraic structure for higher categorical homotopy.

Abstract

For a Kan complex with a vertex, we have the notion of its simplicial homotopy groups. In this paper, for a weak complicial set in the sense of Verity with a vertex, we construct monoids which are a generalization of simplicial homotopy groups.