%0 Journal Article
%T Categorical methods in Hopf algebras
%A Wang Dingguo
%A Yang Shilin
%A Ji Qingzhong
%J Tamkang Journal of Mathematics
%D 2001
%I Tamkang University
%R 10.5556/j.tkjm.32.2001.281-292
%X In this paper, we first study the adjoint relationship of general functors between two Grothendieck categories. Then apply those results to obtain information about the connections of the categories $ A # H $-mod and $ A^H $-mod, resp. $ {cal M}^{C times H} $ and $ {cal M}^{C^{coH}} $, where $ A $ is an $ H $-module algebra and $ C $ is an $ H $-comodule coalgebra. In particular, the relationships between the (co)generators, injectivity and projectivity of $ A # H $-modules and the corresponding property of $ A^H $-modules are given, the relationships between the injective dimension $ A_A $ the corresponding dimension of $ A_{A^H}^H $ and $ A # H_{A # H} $ are also established.
%U http://journals.math.tku.edu.tw/index.php/TKJM/article/view/343