{"paper":{"title":"Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.RA"],"primary_cat":"math.CT","authors_text":"Leonid Positselski","submitted_at":"2025-09-09T12:12:42Z","abstract_excerpt":"Given a hereditary complete cotorsion pair $(\\mathsf A,\\mathsf B)$ generated by a set of objects in a Grothendieck category $\\mathsf K$, we construct a natural equivalence between the Becker coderived category of the left-hand class $\\mathsf A$ and the Becker contraderived category of the right-hand class $\\mathsf B$. We show that a nested pair of cotorsion pairs $(\\mathsf A_1,\\mathsf B_1)\\le(\\mathsf A_2,\\mathsf B_2)$ provides an adjunction between the related co/contraderived categories, which is induced by a Quillen adjunction between abelian model structures. Then we specialize to the cotor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07645","kind":"arxiv","version":3},"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/2509.07645/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"}