Homotopy theory of monoids and derived localization

Lazarev, Andrey and Holstein, Julian and Chuang, Joseph (2021) Homotopy theory of monoids and derived localization. Journal of Homotopy and Related Structures. ISSN 2193-8407

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Abstract

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