@article{Dingguo_Shilin_Qingzhong_2001, title={Categorical methods in Hopf algebras}, volume={32}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/343}, DOI={10.5556/j.tkjm.32.2001.343}, abstractNote={<p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: black; font-family: Verdana;" lang="EN-US">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 \rtimes 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.</span><span style="font-size: 7.5pt;" lang="EN-US"></span></p>}, number={4}, journal={Tamkang Journal of Mathematics}, author={Dingguo, Wang and Shilin, Yang and Qingzhong, Ji}, year={2001}, month={Dec.}, pages={281–292} }