论文标题
用截短的摩尔复合物的简单基团的扭转理论
Torsion theories of simplicial groups with truncated Moore complex
论文作者
论文摘要
我们在简单组中引入了线性有序的晶格$μ（GRP）$。扭转理论是定义的，而在摩尔复合物上方/下方有界限的简单组分别给出了无扭转/无扭转的子类别。这些扭转理论自然地扩展了组内部组的扭转理论。由于可以计算为扭力小组的标准，因此建立了该晶格与同型组的连接。
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.
