{"paper":{"title":"Completeness of the induced cotorsion pairs in functor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.RT","authors_text":"Fei Xu, Li Liang, Liping Li, Zhenxing Di","submitted_at":"2021-02-11T03:11:59Z","abstract_excerpt":"This paper focuses on a question raised by Holm and J{\\o}rgensen, who asked if the induced cotorsion pairs $(\\Phi({\\sf X}),\\Phi({\\sf X})^{\\perp})$ and $(^{\\perp}\\Psi({\\sf Y}),\\Psi({\\sf Y}))$ in $\\mathrm{Rep}(Q,{\\sf{A}})$ -- the category of all $\\sf{A}$-valued representations of a quiver $Q$ -- are complete whenever $(\\sf X,\\sf Y)$ is a complete cotorsion pair in an abelian category $\\sf{A}$ satisfying some mild conditions. Recently, Odaba\\c{s}{\\i} gave an affirmative answer if the quiver $Q$ is rooted and the cotorsion pair $(\\sf X,\\sf Y)$ is further hereditary. In this paper, we improve Odaba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05826","kind":"arxiv","version":4},"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/2102.05826/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"}