构造余环上的辫子张量范畴

Construction of Braided Monoidal Category over a Coring

探讨了余环上的余模范畴如何构成辫子张量范畴.首先假设C是一个余环,则由C构成C上的余模可得余模范畴成为张量范畴的条件.其条件是要求问题中的余环和代数必须为双环和双代数且满足某些相容条件.然后在给定的张量余模范畴上通过一个扭曲卷积可逆映射定义辫子,并探讨得到余环上的余模范畴构成辫子张量范畴的充分必要条件.缠绕模范畴是余环上的余模范畴的一个特例,可将余环上的余模范畴得到的结果应用到缠绕模范畴中.

The purpose of this paper is to investigate how the category of the comodules of the coring can be made into a braided monoidal category.Firstly,the conditions making the category into a monoidal category are obtained by using the fact that if C is a coring,then C can be made into a C-comodule.The conditions are that the algebra and coring in question are bialgebra and bi-ring,with some extra compatibility relations.Then,given a monodial category of comodules of the coring,the braiding is constructed by means of a twisted convolution invertible map and the sufficient and necessary conditions making the category form into a braided monoidal category are obtained.The category of entwined modules is contained in the category of the comodules of the coring.Lastly,the construction can be applied to the category of entwined modules as an example.