相关Hopf模范畴_L^LYD_B^A与范畴_L^LYD_(B_0)的等价性

Discussion of Equivalence Between the Relative Hopf-Module Category _L^LYD_B^A and Category _L^LYD_(B_0)

设L,A是域k上的Hopf代数,B是右A-余模代数。在Yetter-Drinfeld范畴的基础上,定义一类相关Hopf模范畴LLYDAB以及范畴LLYDB,当B是右内射A-余模代数时,给出范畴LLYDBA与LLYDB等价的一个条件。

Let L and A be Hopf algebras on field k, B a right A - comodule algebra, we define a sort of category L^L YDB^A called the relative Hopf module category, and another category L^L YDBO is also defined, which both are based on the defination of Yetter - Drinfeld category. An equvalence condition between L^LYDB^A and L^LYDBO is given when B is a right injective A - comodule algebra.