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Categories of modules, comodules and contramodules over representations

Balodi, M and Banerjee, A and Ray, S (2023) Categories of modules, comodules and contramodules over representations. In: Forum Mathematicum .

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Official URL: https://doi.org/10.1515/forum-2023-0043


We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical framework which incorporates all adjoint functors between these categories in a natural manner. Various classical properties of coalgebras and their morphisms arise naturally within this theory. We also consider cartesian objects in each of these categories, which may be viewed as counterparts of quasi-coherent sheaves over a scheme. We study their categorical properties using cardinality arguments. Our focus is on generators for these categories and on Grothendieck categories, because the latter may be treated as replacements for noncommutative spaces. © 2023 Walter de Gruyter GmbH, Berlin/Boston 2023.

Item Type: Journal Article
Publication: Forum Mathematicum
Publisher: Walter de Gruyter GmbH
Additional Information: The copyright for this article belongs to the Walter de Gruyter GmbH.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 28 Oct 2023 09:30
Last Modified: 28 Oct 2023 09:30
URI: https://eprints.iisc.ac.in/id/eprint/83146

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