交叉点范畴及其等变化
Crossed pointed categories and their equivariantizations
摘要：
本文提出交叉模的拟交换第三上同调的概念，推广了Eilenberg和MacLane的交换上同调和Obern的拟交换上同调，并利用它对交叉点范畴进行了分类，对后者应用等变化过程得到了辫子融合范畴，它可以看作是有限群的扭曲Drinfeld双上模范畴的推广.作为一个结果，我们得到的所有辫子群理论范畴的描述。给出了这些范畴是模范畴的一个判别准则。我们还描述了这些范畴下的拟三角拟霍普夫代数。
英文摘要：
We propose the notion of quasi-abelian third cohomology of crossed modules, generalizing Eilenberg and MacLane's abelian cohomology and Ospel's quasi-abelian cohomology, and classify crossed pointed categories in terms of it. We apply the process of equivariantization to the latter to obtain braided fusion categories which may be viewed as generalizations of the categories of modules over twisted Drinfeld doubles of finite groups. As a consequence, we obtain a description of all braided group-theoretical categories. A criterion for these categories to be modular is given. We also describe the quasi-triangular quasi-Hopf algebras underlying these categories.
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。
