Homotopy theory of monoids and derived localization

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 $$\infty $$ ∞ -category of discrete monoids.