{"paper":{"title":"Completeness of the induced cotorsion pairs in categories of quiver representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CT","authors_text":"Sinem Odabasi","submitted_at":"2017-11-01T23:20:35Z","abstract_excerpt":"Given a complete hereditary cotorsion pair $(\\mathcal{A}, \\mathcal{B})$ in an abelian category $\\mathcal{C}$ satisfying certain conditions, we study the completeness of the induced cotorsion pairs $(\\Phi(\\mathcal{A}), \\Phi(\\mathcal{A})^{\\perp})$ and $(^{\\perp}\\Psi(\\mathcal{B}), \\Psi(\\mathcal{B}) )$ in the category $\\mbox{Rep}(Q, \\mathcal{C})$ of $\\mathcal{C}$-valued representations of a given quiver $Q$. We show that if $Q$ is left rooted, then the cotorsion pair $(\\Phi(\\mathcal{A}), \\Phi(\\mathcal{A})^{\\perp})$ is complete, and if $Q$ is right rooted, then the cotorsion pair $(^{\\perp}\\Psi(\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00559","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":""},"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"}