余模范畴上的强等价(英)  

Strong Equivalence for Categories of Comodules

作　　者：吴章清[1] 崔杰[1] 

机构地区：[1]复旦大学数学研究所

出　　处：《复旦学报（自然科学版）》1998年第5期644-650,共7页Journal of Fudan University：Natural Science

摘　　要：证明了h（－，M）函数保持右正合及有限直和，-□cM（cM拟有限）保持拟有限和有限维性；推出了联系余-hom和余张量函数的一个同构．给出了强等价新的定义，并得到范畴Mct和MD强等价当且仅当cM和DM强等价．令F：c*M→D*M是一等价，则当F(Mc)MD时，F|Mc强等价．这改进了林的结果．作为应用，证明了若F同上且D是自反的，则F|Mc是一强等价，且C是上自反的．This paper mainly discusses the strong equivalence of categories of comodules. It is proved that h(-,M) preserves right exact and finite direct sums, and -□cM (cM is quasifinite) preserves quasi-finite and finite dimensionality. And an isomorphism,which connects the co-hom and co-tensor functors is derived. A new definition of the strong equivalence is given, and it is shown that Mc and MD are strong equivalent if and only if cM and DM are. Set F: c*M→D*. M be an equivalent functor. Then if F (Mc)MD, F |Mc is a strong equivalence. It has improved Lin's result on strong equivalence. As an application, if D is coreflexive, then F |Mc is a strong equivalence and C is coreflexive.

关 键 词：余代数 余模 余-hom 余张量 范畴等价 强等价 

分 类 号：O153.3[理学—数学]