{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EJHEOBHLS4ZCFK7EWEA3GJFMY4","short_pith_number":"pith:EJHEOBHL","schema_version":"1.0","canonical_sha256":"224e4704eb973222abe4b101b324acc724559d72024f5f2bc00a9572a6fee9b2","source":{"kind":"arxiv","id":"1308.1551","version":1},"attestation_state":"computed","paper":{"title":"Injective Objects of Monomorphism Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Keyan Song, Yuehui Zhang, Zhanping Wang","submitted_at":"2013-08-07T12:38:22Z","abstract_excerpt":"For an acyclic quiver $Q$ and a finite-dimensional algebra $A$, we give a unified form of the indecomposable injective objects in the monomorphism category ${\\rm Mon}(Q,A)$ and prove that ${\\rm Mon}(Q, A)$ has enough injective objects. As applications, we show that for a given self-injective algebra $A$, a tilting object in the stable category $\\underline{A}$-mod induces a natural tilting object in the stable monomorphism category $\\underline{\\rm Mon}(Q,A)$. We also realize the singularity category of the algebra $kQ\\otimes_k A$ as the stable monomorphism category of the module category of $A$"},"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":"1308.1551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-08-07T12:38:22Z","cross_cats_sorted":[],"title_canon_sha256":"853c9bcfbfeb328d62e092393a050a4c39487c787dc3fb8c04059e17c82be617","abstract_canon_sha256":"993f717bc55d51789f615f4ded51a4e44da2e3df553fe0619c9ef396e0dc84e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:30.869258Z","signature_b64":"gdASc61x+v9lBUr8vX9UFUXgmcllCFllVXAWTB8f9clzkWRVpLth4VNe3qjQsYB4aH9fp7A0K3mKg0tN4NsDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"224e4704eb973222abe4b101b324acc724559d72024f5f2bc00a9572a6fee9b2","last_reissued_at":"2026-05-18T03:16:30.868679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:30.868679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Injective Objects of Monomorphism Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Keyan Song, Yuehui Zhang, Zhanping Wang","submitted_at":"2013-08-07T12:38:22Z","abstract_excerpt":"For an acyclic quiver $Q$ and a finite-dimensional algebra $A$, we give a unified form of the indecomposable injective objects in the monomorphism category ${\\rm Mon}(Q,A)$ and prove that ${\\rm Mon}(Q, A)$ has enough injective objects. As applications, we show that for a given self-injective algebra $A$, a tilting object in the stable category $\\underline{A}$-mod induces a natural tilting object in the stable monomorphism category $\\underline{\\rm Mon}(Q,A)$. We also realize the singularity category of the algebra $kQ\\otimes_k A$ as the stable monomorphism category of the module category of $A$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1551","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":"1308.1551","created_at":"2026-05-18T03:16:30.868774+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.1551v1","created_at":"2026-05-18T03:16:30.868774+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1551","created_at":"2026-05-18T03:16:30.868774+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJHEOBHLS4ZC","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJHEOBHLS4ZCFK7E","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJHEOBHL","created_at":"2026-05-18T12:27:43.054852+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/EJHEOBHLS4ZCFK7EWEA3GJFMY4","json":"https://pith.science/pith/EJHEOBHLS4ZCFK7EWEA3GJFMY4.json","graph_json":"https://pith.science/api/pith-number/EJHEOBHLS4ZCFK7EWEA3GJFMY4/graph.json","events_json":"https://pith.science/api/pith-number/EJHEOBHLS4ZCFK7EWEA3GJFMY4/events.json","paper":"https://pith.science/paper/EJHEOBHL"},"agent_actions":{"view_html":"https://pith.science/pith/EJHEOBHLS4ZCFK7EWEA3GJFMY4","download_json":"https://pith.science/pith/EJHEOBHLS4ZCFK7EWEA3GJFMY4.json","view_paper":"https://pith.science/paper/EJHEOBHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.1551&json=true","fetch_graph":"https://pith.science/api/pith-number/EJHEOBHLS4ZCFK7EWEA3GJFMY4/graph.json","fetch_events":"https://pith.science/api/pith-number/EJHEOBHLS4ZCFK7EWEA3GJFMY4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJHEOBHLS4ZCFK7EWEA3GJFMY4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJHEOBHLS4ZCFK7EWEA3GJFMY4/action/storage_attestation","attest_author":"https://pith.science/pith/EJHEOBHLS4ZCFK7EWEA3GJFMY4/action/author_attestation","sign_citation":"https://pith.science/pith/EJHEOBHLS4ZCFK7EWEA3GJFMY4/action/citation_signature","submit_replication":"https://pith.science/pith/EJHEOBHLS4ZCFK7EWEA3GJFMY4/action/replication_record"}},"created_at":"2026-05-18T03:16:30.868774+00:00","updated_at":"2026-05-18T03:16:30.868774+00:00"}