Banerjee, A (2023) Entwined Modules Over Representations of Categories. In: Algebras and Representation Theory .
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Abstract
We introduce a theory of modules over a representation of a small category taking values in entwining structures over a semiperfect coalgebra. This takes forward the aim of developing categories of entwined modules to the same extent as that of module categories as well as the philosophy of Mitchell of working with rings with several objects. The representations are motivated by work of Estrada and Virili, who developed a theory of modules over a representation taking values in small preadditive categories, which were then studied in the same spirit as sheaves of modules over a scheme. We also describe, by means of Frobenius and separable functors, how our theory relates to that of modules over the underlying representation taking values in small K-linear categories.
| Item Type: | Journal Article |
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| Publication: | Algebras and Representation Theory |
| Publisher: | Springer Science and Business Media B.V. |
| Additional Information: | The copyright for this article belongs to the Author. |
| Keywords: | Coalgebras; Entwined modules; Entwining structures; Frobenii pair; Functors; Linear categories; Ring with several object; Separable functor, Algebra |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 06 Jul 2023 06:22 |
| Last Modified: | 06 Jul 2023 06:22 |
| URI: | https://eprints.iisc.ac.in/id/eprint/82131 |
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