论文标题
迭代暂停的认可原则，作为小立方体的山地
A recognition principle for iterated suspensions as coalgebras over the little cubes operad
论文作者
论文摘要
我们的主要结果是迭代悬架作为小磁盘作业的煤层的认可原则。鉴于拓扑作业，我们在带有楔形产品的尖式拓扑空间中构建了一个ComOnad。然后，我们证明了一个近似定理，该定理表明与小$ n $ -incubes Operad相关的comoNAD与ComOnad $σ^nΩ^n $相当于悬架环空间相邻引起的comonad $σ^nΩ^n $。最后，我们的认可定理指出，每个小$ n $ aupbes calgebra均与$ n $折的悬架相同。这些结果是5月在迭代环空间上的基础结果的Eckmann-希尔顿双重。
Our main result is a recognition principle for iterated suspensions as coalgebras over the little disks operads. Given a topological operad, we construct a comonad in pointed topological spaces endowed with the wedge product. We then prove an approximation theorem that shows that the comonad associated to the little $n$-cubes operad is weakly equivalent to the comonad $Σ^n Ω^n$ arising from the suspension-loop space adjunction. Finally, our recognition theorem states that every little $n$-cubes coalgebra is homotopy equivalent to an $n$-fold suspension. These results are the Eckmann--Hilton dual of May's foundational results on iterated loop spaces.
