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arXiv · 2410.17852

Entwined comodules and contramodules over coalgebras with several objects: Frobenius, separability and Maschke theorems

Abhishek Banerjee·Surjeet Kour
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Abstract

We study module like objects over categorical quotients of algebras by the action of coalgebras with several objects. These take the form of ``entwined comodules'' and ``entwined contramodules'' over a triple $(\mathscr C,A,\psi)$, where $A$ is an algebra, $\mathscr C$ is a coalgebra with several objects and $\psi$ is a collection of maps that ``entwines'' $\mathscr C$ with $A$. Our objective is to prove Frobenius, separability and Maschke type theorems for functors between categories of entwined comodules and entwined contramodules.

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Abhishek Banerjee, Surjeet Kour. 2024-10-23. Entwined comodules and contramodules over coalgebras with several objects: Frobenius, separability and Maschke theorems. https://arxiv.org/abs/2410.17852

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