{"paper":{"title":"An explicit self-dual construction of complete cotorsion pairs in the relative context","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Leonid Positselski","submitted_at":"2020-06-02T16:59:51Z","abstract_excerpt":"Let $R\\to A$ be a homomorphism of associative rings, and let $(\\mathcal F,\\mathcal C)$ be a hereditary complete cotorsion pair in $R\\mathsf{-Mod}$. Let $(\\mathcal F_A,\\mathcal C_A)$ be the cotorsion pair in $A\\mathsf{-Mod}$ in which $\\mathcal F_A$ is the class of all left $A$-modules whose underlying $R$-modules belong to $\\mathcal F$. Assuming that the $\\mathcal F$-resolution dimension of every left $R$-module is finite and the class $\\mathcal F$ is preserved by the coinduction functor $\\operatorname{Hom}_R(A,-)$, we show that $\\mathcal C_A$ is the class of all direct summands of left $A$-mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.01778","kind":"arxiv","version":7},"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/2006.01778/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"}