标题： 第三上同调2-群 显示英文标题

标题： The third cohomology 2-group

摘要： 在本文中，我们证明一个保持有限乘积的张量纤维可以通过一个具有相同性质但具有群轨道纤维的张量纤维进行分解。如果余域是加性的，可以为新张量纤维的每个纤维赋予一个规范的对称2-群结构。然后我们将这种分解应用于将群的交叉扩张C映射到其对应的C-模的张量纤维。由此在纤维上获得的对称2-群结构定义了以C-模为系数的C的第三上同调2-群。我们证明通常的第三和第二上同调群作为其同伦不变量被恢复。此外，尽管所有结果都在群的范畴中呈现，但一旦采用相应的内部概念，它们的证明在任何强原型模的半阿贝尔范畴中都是有效的。 显示英文摘要

摘要： In this paper we show that a finite product preserving opfibration can be factorized through an opfibration with the same property, but with groupoidal fibres. If moreover the codomain is additive, one can endow each fibre of the new opfibration with a canonical symmetric 2-group structure. We then apply such factorization to the opfibration that sends a crossed extension of a group C to its corresponding C-module. The symmetric 2-group structure so obtained on the fibres, defines the third cohomology 2-group of C, with coefficients in a C-module. We show that the usual third and second cohomology groups are recovered as its homotopy invariants. Furthermore, even if all results are presented in the category of groups, their proofs are valid in any strongly protomodular semi-abelian category, once one adopts the corresponding internal notions.