Homological Epimorphisms and Hochschild-Mitchell Cohomology
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912821646721024 |
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| author | Santiago-Vargas, V. Velasco-Páez, E. O. |
| author_facet | Santiago-Vargas, V. Velasco-Páez, E. O. |
| contents | In this work, we study the Hochschild-Mitchell Cohomology of triangular matrix categories. Given a triangular matrix category $Λ=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$, we investigate the relationship of the Hochschild-Mitchell cohomologies $H^{i}(Λ)$ and $H^{i}(\mathcal{U})$ of $Λ$ and $\mathcal{U}$ respectively; and we show that they can be connected by a long exact sequence. This result extend the well-known result of Michelana-Platzeck given in [S. Michelena, M. I. Platzeck. {\it{Hochschild cohomology of triangular matrix algebras}}. J. Algebra 233, (2000) 502-525]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03554 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homological Epimorphisms and Hochschild-Mitchell Cohomology Santiago-Vargas, V. Velasco-Páez, E. O. Representation Theory Category Theory K-Theory and Homology In this work, we study the Hochschild-Mitchell Cohomology of triangular matrix categories. Given a triangular matrix category $Λ=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$, we investigate the relationship of the Hochschild-Mitchell cohomologies $H^{i}(Λ)$ and $H^{i}(\mathcal{U})$ of $Λ$ and $\mathcal{U}$ respectively; and we show that they can be connected by a long exact sequence. This result extend the well-known result of Michelana-Platzeck given in [S. Michelena, M. I. Platzeck. {\it{Hochschild cohomology of triangular matrix algebras}}. J. Algebra 233, (2000) 502-525]. |
| title | Homological Epimorphisms and Hochschild-Mitchell Cohomology |
| topic | Representation Theory Category Theory K-Theory and Homology |
| url | https://arxiv.org/abs/2303.03554 |