Realization functors in algebraic triangulated categories
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910907928412160 |
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| author | Letz, Janina C. Sauter, Julia |
| author_facet | Letz, Janina C. Sauter, Julia |
| contents | Let $\mathcal{T}$ be an algebraic triangulated category and $\mathcal{C}$ an extension-closed subcategory with $\operatorname{Hom}(\mathcal{C}, Σ^{<0} \mathcal{C})=0$. Then $\mathcal{C}$ has an exact structure induced from exact triangles in $\mathcal{T}$. Keller and Vossieck say that there exists a triangle functor $\operatorname{D}^b(\mathcal{C}) \to \mathcal{T}$ extending the inclusion $\mathcal{C} \subseteq \mathcal{T}$. We provide the missing details for a complete proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Realization functors in algebraic triangulated categories Letz, Janina C. Sauter, Julia Representation Theory 18G80 18G35 Let $\mathcal{T}$ be an algebraic triangulated category and $\mathcal{C}$ an extension-closed subcategory with $\operatorname{Hom}(\mathcal{C}, Σ^{<0} \mathcal{C})=0$. Then $\mathcal{C}$ has an exact structure induced from exact triangles in $\mathcal{T}$. Keller and Vossieck say that there exists a triangle functor $\operatorname{D}^b(\mathcal{C}) \to \mathcal{T}$ extending the inclusion $\mathcal{C} \subseteq \mathcal{T}$. We provide the missing details for a complete proof. |
| title | Realization functors in algebraic triangulated categories |
| topic | Representation Theory 18G80 18G35 |
| url | https://arxiv.org/abs/2412.07455 |