Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology of modules over $H$-categories and co-$H$-categories   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 $Hom$ objects and higher derived functors of coinvariants.

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The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat