{"paper":{"title":"Quotient categories with exact structure from $(n+2)$-rigid subcategories in extriangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Corina S\\'aenz, Mindy Y. Huerta, Octavio Mendoza, Valente Santiago","submitted_at":"2023-09-25T23:21:44Z","abstract_excerpt":"In this work we introduce the notion of higher $\\mathbb{E}$-extension groups for an extriangulated category $\\mathcal{C}$ and study the quotients $\\mathcal{X}_{n+1}^{\\vee}/[\\mathcal{X}]$ and $\\mathcal{X}_{n+1}^{\\wedge}/[\\mathcal{X}]$ when $\\mathcal{X}$ is an $(n+2)$-rigid subcategory of $\\mathcal{C}$. We also prove (under mild conditions) that each one is equivalent to a suitable subcategory of the category of functors of the stable category of $\\mathcal{X}_{n}^{\\vee}$ and the co-stable category of $\\mathcal{X}_{n}^{\\wedge}$, respectively. Moreover, it can be induced an exact structure through"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.14576","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/2309.14576/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"}