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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2406.19883 |
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| _version_ | 1866914610002526208 |
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| author | Wu, Mawei |
| author_facet | Wu, Mawei |
| contents | Let $\mathcal {C}$ be a small category and let $R$ be a representation of the category $\mathcal {C}$, that is, a pseudofunctor from a small category to the category of small preadditive categories. In this paper, we mainly study the category $\mbox{Mod-} R$ of right modules over $R$. We characterize it both as a category of the Abelian group valued functors on $Gr(R)$ and as a category of modules over a new family of algebras: the pseudoskew category algebras $R[{\mathcal C}]$, where $Gr(R)$ is the linear Grothendieck construction of $R$. Moreover, we also classify the hereditary torsion pairs in $\mbox{Mod-} R$ and reprove Theorem 3.18 of the paper (S. Estrada and S. Virili. Cartesian modules over representations of small categories. Adv. in Math. 310: 557-609, 2017) of Estrada and Virili. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19883 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pseudoskew category algebras and modules over representations of small categories Wu, Mawei Representation Theory Let $\mathcal {C}$ be a small category and let $R$ be a representation of the category $\mathcal {C}$, that is, a pseudofunctor from a small category to the category of small preadditive categories. In this paper, we mainly study the category $\mbox{Mod-} R$ of right modules over $R$. We characterize it both as a category of the Abelian group valued functors on $Gr(R)$ and as a category of modules over a new family of algebras: the pseudoskew category algebras $R[{\mathcal C}]$, where $Gr(R)$ is the linear Grothendieck construction of $R$. Moreover, we also classify the hereditary torsion pairs in $\mbox{Mod-} R$ and reprove Theorem 3.18 of the paper (S. Estrada and S. Virili. Cartesian modules over representations of small categories. Adv. in Math. 310: 557-609, 2017) of Estrada and Virili. |
| title | Pseudoskew category algebras and modules over representations of small categories |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2406.19883 |