Homotopy theory of monoids and derived localization

TL;DR

This paper applies derived localization techniques to classical algebraic topology constructions, offering simplified proofs and new models for understanding the homotopy theory of spaces and monoids.

Contribution

It introduces a novel approach using derived localization to unify and simplify proofs of key results and proposes a new model for the homotopy theory of connected spaces via monoids.

Findings

Simplified proofs of generalized Adams' cobar-construction

A new model for homotopy theory of connected spaces

Application of derived localization to classical topological constructions

Abstract

We use derived localization of the bar and nerve constructions to provide simple proofs of a number of results in algebraic topology. This includes a recent generalization of Adams' cobar-construction to the non-simply connected case, and a new model for the homotopy theory of connected topological spaces using an infinity category of discrete monoids.