Standard $t$-structures
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916683168350208 |
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| author | Haine, Peter J. Porta, Mauro Teyssier, Jean-Baptiste |
| author_facet | Haine, Peter J. Porta, Mauro Teyssier, Jean-Baptiste |
| contents | We provide a general construction of induced $t$-structures, that generalizes standard $t$-structures for $\infty$-categories of sheaves. More precisely, given a presentable $\infty$-category $\mathcal{X}$ and a presentable stable $\infty$-category $\mathcal{E}$ equipped with an accessible $t$-structure $τ= (\mathcal{E}_{\geq 0}, \mathcal{E}_{\leq 0})$, we show that $\mathcal{X} \otimes \mathcal{E}$ is equipped with a canonical $t$-structure whose coconnective part is given in $\mathcal{X} \otimes \mathcal{E}_{\leq 0}$. When $\mathcal{X}$ is an $\infty$-topos, we give a more explicit description of the connective part as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Standard $t$-structures Haine, Peter J. Porta, Mauro Teyssier, Jean-Baptiste Category Theory Algebraic Topology We provide a general construction of induced $t$-structures, that generalizes standard $t$-structures for $\infty$-categories of sheaves. More precisely, given a presentable $\infty$-category $\mathcal{X}$ and a presentable stable $\infty$-category $\mathcal{E}$ equipped with an accessible $t$-structure $τ= (\mathcal{E}_{\geq 0}, \mathcal{E}_{\leq 0})$, we show that $\mathcal{X} \otimes \mathcal{E}$ is equipped with a canonical $t$-structure whose coconnective part is given in $\mathcal{X} \otimes \mathcal{E}_{\leq 0}$. When $\mathcal{X}$ is an $\infty$-topos, we give a more explicit description of the connective part as well. |
| title | Standard $t$-structures |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2504.07473 |