Resolving resolution dimensions in triangulated categories
Let T{\mathcal{T}} be a triangulated category with a proper class ξ\xi of triangles and X{\mathcal{X}} be a subcategory of T{\mathcal{T}}. We first introduce the notion of X{\mathcal{X}}-resolution dimensions for a resolving subcategory of T{\mathcal{T}} and then give some descriptions of objects h...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/734d471faeec407e8b816d04385e0357 |
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| Sumario: | Let T{\mathcal{T}} be a triangulated category with a proper class ξ\xi of triangles and X{\mathcal{X}} be a subcategory of T{\mathcal{T}}. We first introduce the notion of X{\mathcal{X}}-resolution dimensions for a resolving subcategory of T{\mathcal{T}} and then give some descriptions of objects having finite X{\mathcal{X}}-resolution dimensions. In particular, we obtain Auslander-Buchweitz approximations for these objects. As applications, we construct adjoint pairs for two kinds of inclusion functors and characterize objects having finite X{\mathcal{X}}-resolution dimensions in terms of a notion of ξ\xi -cellular towers. We also construct a new resolving subcategory from a given resolving subcategory and reformulate some known results. |
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