严格三次Ω-范畴的空间型上的Moore超矩形

Cubical rigidification, the cobar construction, and the based loop space

We prove the following generalization of a classical result of Adams: for any pointed and connected topological space $(X,b)$, that is not necessarily simply connected, the cobar construction of the differential graded (dg) coalgebra of normalized singular chains in $X$ with vertices at $b$ is weakly equivalent as a differential graded associative algebra (dga) to the singular chains on the Moore based loop space of $X$ at $b$. We deduce this statement from several more general categorical results of independent interest. We construct a functor $\mathfrak{C}_{\square_c}$ from simplicial sets t…

通过A∞-函子比较dg范畴模型用于路径空间

Comparing dg category models for path spaces via $A_\infty$-functors

通过A∞-函子比较dg范畴模型用于路径空间，构建了Chen迭代积分映射的双版本，并证明其在单连通空间中与Adams映射的同伦逆关系。