The derivator of a dg-category
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908478038081536 |
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| author | Genovese, Francesco Sava, Chiara Šťovíček, Jan |
| author_facet | Genovese, Francesco Sava, Chiara Šťovíček, Jan |
| contents | In this work, we construct the stable derivator associated to a homotopically complete and cocomplete dg-category by explicitly defining homotopy Kan extensions via suitable weighted homotopy limits and colimits in dg-categories. By restricting the domain of the derivator to finite direct categories, we obtain a well-defined derivator even for pretriangulated dg-categories. This definition enables an explicit description of the derivator associated to a weakly idempotent complete Frobenius exact category, leading to a more direct characterization in terms of Gorenstein projective (equivalently, Gorenstein injective) diagrams. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The derivator of a dg-category Genovese, Francesco Sava, Chiara Šťovíček, Jan Category Theory Representation Theory Primary: 18G35, 18N40, Secondary: 18G05, 18G80, 16G20 In this work, we construct the stable derivator associated to a homotopically complete and cocomplete dg-category by explicitly defining homotopy Kan extensions via suitable weighted homotopy limits and colimits in dg-categories. By restricting the domain of the derivator to finite direct categories, we obtain a well-defined derivator even for pretriangulated dg-categories. This definition enables an explicit description of the derivator associated to a weakly idempotent complete Frobenius exact category, leading to a more direct characterization in terms of Gorenstein projective (equivalently, Gorenstein injective) diagrams. |
| title | The derivator of a dg-category |
| topic | Category Theory Representation Theory Primary: 18G35, 18N40, Secondary: 18G05, 18G80, 16G20 |
| url | https://arxiv.org/abs/2508.02612 |