范畴M_1~C,M_π~C及M^(C×kπ)的等价性和同构性

The categories equivalence and isomorphism for M_1~C,M_π~C and M^(C×kπ)

设C是π-余代数,主要研究了右C1-余模范畴MC1,右π-C-余模范畴MCπ及右群-C×kπ-余模范畴MC×kπ三者之间的范畴等价性和同构性问题.主要证明了范畴MCπ与MC×kπ同构.进一步若C是强π-余代数,则范畴MC1与MCπ等价,范畴MC1与MCk×π等价.

Let C be a π-coalgebra,We studied the categories equivalence and isomorphism for right C1-comodules category,right group-C-comodules category and π-Ckπ-comodules category.It was mainly proved that the categories MCπ and MCkπ are isomorphism.Furthermore,if C is strong π-coalgebra,then the categories MC1 and MCπ are equivalent,the categories MC1 and MCkπ are equivalent.