单纯形范畴的迭代圈积与迭代闭路空间
Iterated wreath product of the simplex category and iterated loop spaces
摘要：
推广Segal的方法1倍闭路空间，同伦理论的$n$倍闭路空间被证明是等价的同伦理论的约化$Θ_n$ -空间，其中$Θ_n$是一个迭代圈积的单纯形范畴$Δ$。从$Θ_n$到$Γ$的函子序列允许与$Γ$空间相关联的Segal谱的替代描述。特别地，每个Eilenberg-MacLane空间$K(π,n)$具有规范简化的$Θ_n$ -集模型。
英文摘要：
Generalising Segal's approach to 1-fold loop spaces, the homotopy theory of $n$-fold loop spaces is shown to be equivalent to the homotopy theory of reduced $Θ_n$-spaces, where $Θ_n$ is an iterated wreath product of the simplex category $Δ$. A sequence of functors from $Θ_n$ to $Γ$ allows for an alternative description of the Segal-spectrum associated to a $Γ$-space. In particular, each Eilenberg-MacLane space $K(π,n)$ has a canonical reduced $Θ_n$-set model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
