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.

中文翻译：

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id半同伦的同伦理论和衍生的局部化

我们使用杆和神经结构的派生定位来提供已知和新的代数拓扑中的许多结果的简单证明。这包括将Adams的cobar构造最近推广到非简单连通的情况，以及将连通拓扑空间的同构理论作为\（\ infty \） -离散半分体的类别的新代数模型。