Functor categories, Recollements, Triangular Matrix category
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916961740390400 |
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| author | Sandoval-Miranda, M. L. S. Santiago-Vargas, V. Velasco-Páez, E. O. |
| author_facet | Sandoval-Miranda, M. L. S. Santiago-Vargas, V. Velasco-Páez, E. O. |
| contents | In this paper we study triangular matrix categories using the theory of recollements of abelian categories. Given a triangular matrix category we construct two canonical recollements. We show that if certain funtors of these recollements are exact then the category appearing in the middle term is actually a triangular matrix category. This result is a generalization of one given by Liping Li in \cite{LipingLi}. We also show that if $\mathrm{Mod}(\mathcal{C})$ admits a nontrivial torsion pair by abelian categories then $\mathcal{C}$ is equivalent to a triangular matrix category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Functor categories, Recollements, Triangular Matrix category Sandoval-Miranda, M. L. S. Santiago-Vargas, V. Velasco-Páez, E. O. Representation Theory Category Theory Rings and Algebras In this paper we study triangular matrix categories using the theory of recollements of abelian categories. Given a triangular matrix category we construct two canonical recollements. We show that if certain funtors of these recollements are exact then the category appearing in the middle term is actually a triangular matrix category. This result is a generalization of one given by Liping Li in \cite{LipingLi}. We also show that if $\mathrm{Mod}(\mathcal{C})$ admits a nontrivial torsion pair by abelian categories then $\mathcal{C}$ is equivalent to a triangular matrix category. |
| title | Functor categories, Recollements, Triangular Matrix category |
| topic | Representation Theory Category Theory Rings and Algebras |
| url | https://arxiv.org/abs/2509.18290 |