Gorenstein categories relative to G-admissible triples
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913695653691392 |
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| author | Estrada, Sergio Mendoza, Octavio Pérez, Marco A. |
| author_facet | Estrada, Sergio Mendoza, Octavio Pérez, Marco A. |
| contents | We present the notion of Gorenstein categories relative to G-admissible triples. This is a relativization of the concept of Gorenstein category (an abelian category with enough projective and injective objects, in which the suprema of the sets $\{ {\rm pd}(I) \ \text{:} \ I \text{ is injective} \}$ and $\{ {\rm id}(P) \ \text{:} \ P \text{ is projective} \}$ are finite). Such categories turn out to be a suitable setting on which it is possible to obtain hereditary abelian model structures where the (co)fibrant objects are Gorenstein injective (resp., Gorenstein projective) objects relative to GI-admissible (resp., GP-admissible) pairs. Applications and examples of these structures are given. Moreover, we link relative Gorenstein categories with tilting theory and obtain relations between different relative homological dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gorenstein categories relative to G-admissible triples Estrada, Sergio Mendoza, Octavio Pérez, Marco A. Category Theory Representation Theory 16E65, 18E10, 14F06, 18G20, 18N40 We present the notion of Gorenstein categories relative to G-admissible triples. This is a relativization of the concept of Gorenstein category (an abelian category with enough projective and injective objects, in which the suprema of the sets $\{ {\rm pd}(I) \ \text{:} \ I \text{ is injective} \}$ and $\{ {\rm id}(P) \ \text{:} \ P \text{ is projective} \}$ are finite). Such categories turn out to be a suitable setting on which it is possible to obtain hereditary abelian model structures where the (co)fibrant objects are Gorenstein injective (resp., Gorenstein projective) objects relative to GI-admissible (resp., GP-admissible) pairs. Applications and examples of these structures are given. Moreover, we link relative Gorenstein categories with tilting theory and obtain relations between different relative homological dimensions. |
| title | Gorenstein categories relative to G-admissible triples |
| topic | Category Theory Representation Theory 16E65, 18E10, 14F06, 18G20, 18N40 |
| url | https://arxiv.org/abs/2502.12439 |