{"paper":{"title":"Gorenstein categories relative to G-admissible triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CT","authors_text":"Marco A. P\\'erez, Octavio Mendoza, Sergio Estrada","submitted_at":"2025-02-18T02:13:14Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.12439","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.12439/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}