【摘要】 研究了如何使entwined模范畴成为辫子张量范畴.首先,利用如果(A,C,ψ)是一个entwining结构,那么AC形成entwined模的结论可以得到entwined模范畴成为张量范畴的充要条件.条件是要求问题中的代数和余代数都必须为双代数而且满足某些相容条件.然后,在给定的张量entwined模范畴上,通过一个扭曲卷积可逆映射Q定义了辫子,并且由类似的方法得到使entwined模范畴构成辫子张量范畴的充分必要条件.最后,作为示例将得到的结果应用到Doi-Hopf模和(α,β)-Yetter-Drinfeld模范畴中.更多还原

【Abstract】 The question of how the category of entwined modules can be made into a braided monoidal category is studied.First,the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if(A,C,ψ)is an entwining structure,then AC can be made into an entwined module.The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations.Then given a monodial category of entwined modules,the braiding is constructed by means of a twisted convolution invertible map Q,and the conditions making the category form into a braided monoidal category are obtained similarly.Finally,the construction is applied to the category of Doi-Hopf modules and(α,β)-Yetter-Drinfeld modules as examples.更多还原