Linear Reedy categories, quasi-hereditary algebras and model structures
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918144555089920 |
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| author | Dalezios, Georgios Stovicek, Jan |
| author_facet | Dalezios, Georgios Stovicek, Jan |
| contents | We study linear versions of Reedy categories in relation with finite dimensional algebras and abelian model structures. We prove that, for a linear Reedy category $\mathcal{C}$ over a field, the category of left $\mathcal{C}$--modules admits a highest weight structure, which in case $\mathcal{C}$ is finite corresponds to a quasi-hereditary algebra with an exact Borel subalgebra. We also lift complete cotorsion pairs and abelian model structures to certain categories of additive functors indexed by linear Reedy categories, generalizing analogous results from the hereditary case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear Reedy categories, quasi-hereditary algebras and model structures Dalezios, Georgios Stovicek, Jan Representation Theory Algebraic Topology Category Theory 16G10, 18N40 (Primary) 16W70, 16G20 (Secondary) We study linear versions of Reedy categories in relation with finite dimensional algebras and abelian model structures. We prove that, for a linear Reedy category $\mathcal{C}$ over a field, the category of left $\mathcal{C}$--modules admits a highest weight structure, which in case $\mathcal{C}$ is finite corresponds to a quasi-hereditary algebra with an exact Borel subalgebra. We also lift complete cotorsion pairs and abelian model structures to certain categories of additive functors indexed by linear Reedy categories, generalizing analogous results from the hereditary case. |
| title | Linear Reedy categories, quasi-hereditary algebras and model structures |
| topic | Representation Theory Algebraic Topology Category Theory 16G10, 18N40 (Primary) 16W70, 16G20 (Secondary) |
| url | https://arxiv.org/abs/2409.06823 |