单群和对称单群的非交换Dold-Kan分解
Nonabelian Dold-Kan Decompositions for Simplicial and Symmetric-Simplicial Groups
摘要：
我们扩展了非交换的Dold-Kan分解的单纯群的Carrasco和Cegarra在两个方面。首先，我们表明，在他们的分解的子群的总顺序属于一个家庭的总订单都引起了多尔-坎分解。我们展示了一个特殊的偏序，使家庭的特点是由所有的全订单扩展偏序。其次，我们考虑的群，并表明，通过使用一个特别选择的介绍的范畴的群，单纯运营商，新的多尔德-坎分解存在代数简单得多比那些Carrasco和Cegarra的意义上说，两个组件的交换子子位于一个单一的组件子群。
英文摘要：
We extend the nonabelian Dold-Kan decomposition for simplicial groups of Carrasco and Cegarra in two ways. First, we show that the total order of the subgroups in their decomposition belongs to a family of total orders all giving rise to Dold-Kan decompositions. We exhibit a particular partial order such that the family is characterized as consisting of all total orders extending the partial order. Second, we consider symmetric-simplicial groups and show that, by using a specially chosen presentation of the category of symmetric-simplicial operators, new Dold-Kan decompositions exist which are algebraically much simpler than those of Carrasco and Cegarra in the sense that the commutator of two component subgroups lies in a single component subgroup.
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