$FI$-modules over preadditive categories and torsion theories

Abhishek Banerjee

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arXiv · 1910.00769

$FI$-modules over preadditive categories and torsion theories

Abhishek Banerjee

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Abstract

We work with $FI$-modules over a small preadditive category $\mathcal R$, viewed as a ring with several objects. Our aim is to study torsion theories for $FI$-modules. We are especially interested in torsion theories on finitely generated $FI$-modules and the category of what we call "shift finitely generated" $FI$-modules. We also apply these methods to study inductive descriptions of $FI$-modules over $\mathcal R$.

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Abhishek Banerjee. 2019-10-02. $FI$-modules over preadditive categories and torsion theories. https://arxiv.org/abs/1910.00769

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