具有截断Moore复形的单纯群的挠理论
Torsion theories of simplicial groups with truncated Moore complex
摘要：
本文在单群中引入扭理论的线性序格$μ(Grp)$。定义了挠理论，其中挠/无挠子范畴分别由具有上/下有界Moore复形的单纯群给出。这些挠理论自然地推广了群中内部群胚的挠理论。由于单纯群的同伦群可以作为挠子代数的幂等元来计算，因此建立了这种格与同伦群的联系。
英文摘要：
We introduce a linearly ordered lattice $μ(Grp)$ of torsion theories in simplicial groups. The torsion theories are defined where the torsion/torsion-free subcategories are given by the simplicial groups with bounded above/below Moore complex, respectively. These torsion theories extend naturally the torsion theories in internal groupoids in groups. Connections of this lattice with the homotopy groups are established since the homotopy groups of a simplicial group can be calculated as the quotients of torsion subojects.
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