Hearts of set-generated t-structures have a set of generators
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913456427368448 |
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| author | Saorín, Manuel |
| author_facet | Saorín, Manuel |
| contents | We show that if $α$ is a regular cardinal, $\mathcal{D}$ is an $α$-compactly generated triangulated category, in the sense of Neeman \cite{N}, and $τ$ is a t-structure in $\mathcal{D}$ generated by a set of $α$-compact objects, then the heart of $τ$ is a locally $α$-presentable (not necessarily Ab5) abelian category. As a consequence, in a well-generated triangulated category any t-structure generated by a set of objects has a heart with a set of generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hearts of set-generated t-structures have a set of generators Saorín, Manuel Category Theory 18G80, 18E10, 18C35, 18E05 We show that if $α$ is a regular cardinal, $\mathcal{D}$ is an $α$-compactly generated triangulated category, in the sense of Neeman \cite{N}, and $τ$ is a t-structure in $\mathcal{D}$ generated by a set of $α$-compact objects, then the heart of $τ$ is a locally $α$-presentable (not necessarily Ab5) abelian category. As a consequence, in a well-generated triangulated category any t-structure generated by a set of objects has a heart with a set of generators. |
| title | Hearts of set-generated t-structures have a set of generators |
| topic | Category Theory 18G80, 18E10, 18C35, 18E05 |
| url | https://arxiv.org/abs/2408.01378 |