Homological epimorphisms in functor categories and singularity categories
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909837104775168 |
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| author | Gutiérrez, Juan Andrés Orozco Vargas, Valente Santiago |
| author_facet | Gutiérrez, Juan Andrés Orozco Vargas, Valente Santiago |
| contents | Given a homological epimorphism $π:\mathcal{C}\longrightarrow \mathcal{C}/\mathcal{I}$ between $K$-categories, we show that if the ideal $\mathcal{I}$ satisfies certain conditions, then there exists an equivalence between the singularity categories $\mathbf{D}_{sg}(\mathrm{Mod}(\mathcal{C}))$ and $ \mathbf{D}_{sg}(\mathrm{Mod}(\mathcal{C}/\mathcal{I}))$. This result generalizes the one obtained by Xiao-Wu Chen in [6]. We apply our result to the one point extension category and show that there is a singular equivalence between a $K$-category $\mathcal{U}$ and its one point extension category $Λ:=\left[ \begin{smallmatrix} \mathcal{C}_{K} & 0 \\ \underline{M} & \mathcal{U} \end{smallmatrix}\right].$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological epimorphisms in functor categories and singularity categories Gutiérrez, Juan Andrés Orozco Vargas, Valente Santiago Representation Theory Category Theory Rings and Algebras Given a homological epimorphism $π:\mathcal{C}\longrightarrow \mathcal{C}/\mathcal{I}$ between $K$-categories, we show that if the ideal $\mathcal{I}$ satisfies certain conditions, then there exists an equivalence between the singularity categories $\mathbf{D}_{sg}(\mathrm{Mod}(\mathcal{C}))$ and $ \mathbf{D}_{sg}(\mathrm{Mod}(\mathcal{C}/\mathcal{I}))$. This result generalizes the one obtained by Xiao-Wu Chen in [6]. We apply our result to the one point extension category and show that there is a singular equivalence between a $K$-category $\mathcal{U}$ and its one point extension category $Λ:=\left[ \begin{smallmatrix} \mathcal{C}_{K} & 0 \\ \underline{M} & \mathcal{U} \end{smallmatrix}\right].$ |
| title | Homological epimorphisms in functor categories and singularity categories |
| topic | Representation Theory Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2510.09855 |