On loop spaces with marking

TL;DR

This paper explores how the construction of loop spaces in Kan complexes can be extended to saturated complicial sets, establishing a connection to monoids within this higher categorical framework.

Contribution

It introduces a method to lift loop space constructions from Kan complexes to saturated complicial sets and relates these to monoids, advancing higher category theory.

Findings

Loop space construction extends to saturated complicial sets.

Establishes a relationship between loop spaces and monoids in complicial sets.

Provides a framework for analyzing homotopy groups in higher categories.

Abstract

An analogous construction of simplicial homotopy group for Kan complex can be applied to saturated complicial sets to give monoids. In this paper, we investigate how the construction of loop spaces of Kan complexes lifts to the complicial setting and relates to such monoids.