Comodules and contramodules over coalgebras associated with locally finite categories

Leonid Positselski

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arXiv · 2307.13358

Comodules and contramodules over coalgebras associated with locally finite categories

Leonid Positselski

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Abstract

We explain how to attach a coalgebra $\mathcal C$ over a field $k$ to a small $k$-linear category $\mathsf E$ satisfying suitable finiteness conditions. In this context, we study full-and-faithfulness of the contramodule forgetful functor, and describe explicitly the categories of locally finite left $\mathcal C$-comodules and left $\mathcal C$-contramodules as certain full subcategories of the category of left $\mathsf E$-modules.

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Leonid Positselski. 2023-07-25. Comodules and contramodules over coalgebras associated with locally finite categories. https://arxiv.org/abs/2307.13358

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