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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.00559","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-11-01T23:20:35Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1cb1ea33e1401fd0c1cdd100ea4b8bc1e03b7c92b08d4c95c9659e8af2e687cb","abstract_canon_sha256":"fd406358fd3f69ce1cb61ae529bf6c96d34b93d37b21625debb27803488d89bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:30.215439Z","signature_b64":"m/Ref2zLmPh33RpkuV3k9Upv0dmJmZeV+KYNjFNsgXmogj7K1+Fmq/Pq69HEKyhBIoILizv+xYBiuRWXhSQfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f46c52d7e05979dfd92e3d755ae20b8461b9043aa5717ae5a41dc041ec3959e","last_reissued_at":"2026-05-18T00:31:30.214875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:30.214875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.00559","created_at":"2026-05-18T00:31:30.214975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.00559v1","created_at":"2026-05-18T00:31:30.214975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00559","created_at":"2026-05-18T00:31:30.214975+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5DMKLL6AWLZ","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5DMKLL6AWLZ37MS","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5DMKLL6","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB","json":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB.json","graph_json":"https://pith.science/api/pith-number/F5DMKLL6AWLZ37MS4PLVLLRAXB/graph.json","events_json":"https://pith.science/api/pith-number/F5DMKLL6AWLZ37MS4PLVLLRAXB/events.json","paper":"https://pith.science/paper/F5DMKLL6"},"agent_actions":{"view_html":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB","download_json":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB.json","view_paper":"https://pith.science/paper/F5DMKLL6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.00559&json=true","fetch_graph":"https://pith.science/api/pith-number/F5DMKLL6AWLZ37MS4PLVLLRAXB/graph.json","fetch_events":"https://pith.science/api/pith-number/F5DMKLL6AWLZ37MS4PLVLLRAXB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB/action/storage_attestation","attest_author":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB/action/author_attestation","sign_citation":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB/action/citation_signature","submit_replication":"https://pith.science/pith/F5DMKLL6AWLZ37MS4PLVLLRAXB/action/replication_record"}},"created_at":"2026-05-18T00:31:30.214975+00:00","updated_at":"2026-05-18T00:31:30.214975+00:00"}