Article contents
Cohomology of Modules Over
$H$-categories and Co-
$H$-categories
Published online by Cambridge University Press: 06 August 2019
Abstract
Let $H$ be a Hopf algebra. We consider
$H$-equivariant modules over a Hopf module category
${\mathcal{C}}$ as modules over the smash extension
${\mathcal{C}}\#H$. We construct Grothendieck spectral sequences for the cohomologies as well as the
$H$-locally finite cohomologies of these objects. We also introduce relative
$({\mathcal{D}},H)$-Hopf modules over a Hopf comodule category
${\mathcal{D}}$. These generalize relative
$(A,H)$-Hopf modules over an
$H$-comodule algebra
$A$. We construct Grothendieck spectral sequences for their cohomologies by using their rational
$\text{Hom}$ objects and higher derived functors of coinvariants.
MSC classification
- Type
- Article
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- Copyright
- © Canadian Mathematical Society 2019
Footnotes
Author M.B. was supported by SERB Fellowship PDF/2017/000229. Author A.B. was partially supported by SERB Matrics fellowship MTR/2017/000112.
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