Geodesic
Cohomology of Modules Over $H$-categories and Co-$H$-categories
Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1352-1385

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/S0008414X19000403
Mots-clés : H-category, co-H-category, H-equivariant module, relative Hopf module 
Balodi, Mamta; Banerjee, Abhishek; Ray, Samarpita. Cohomology of Modules Over $H$-categories and Co-$H$-categories. Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1352-1385. doi: 10.4153/S0008414X19000403
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