{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:T42KFLZGTJJER57F3TWXIP62N2","short_pith_number":"pith:T42KFLZG","schema_version":"1.0","canonical_sha256":"9f34a2af269a5248f7e5dced743fda6ea0d71aaf15ecce5e20ccbfc50fed66b5","source":{"kind":"arxiv","id":"1412.7289","version":1},"attestation_state":"computed","paper":{"title":"From triangulated categories to module categories via homotopical algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Yann Palu","submitted_at":"2014-12-23T08:52:50Z","abstract_excerpt":"The category of modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category C has been given two different descriptions: On the one hand, as shown by Osamu Iyama and Yuji Yoshino, it is equivalent to an ideal quotient of a subcategory of C. On the other hand, Aslak Buan and Robert Marsh proved that this module category is also equivalent to some localisation of C. In this paper, we give a conceptual interpretation, inspired from homotopical algebra, of this double description. Our main aim, yet to be acheived, is to generalise Buan-Marsh's result to the case o"},"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":"1412.7289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-12-23T08:52:50Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"3afac2fe01d821a33da12d9828b09a4a24cb11fd6985dd98f77da045bafd1fe7","abstract_canon_sha256":"9766c7699eb84f38b7157ee66e365d67ae176503d5f56db7499ed8da764e748b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:39.223620Z","signature_b64":"wr5OfWUmEJihL631mLnbX4viim/AysRQR0LX/tOwm+phczxtrDEUM3P2jHGByvoYyT3M6nMHNyCPNZFs1j/cCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f34a2af269a5248f7e5dced743fda6ea0d71aaf15ecce5e20ccbfc50fed66b5","last_reissued_at":"2026-05-18T02:30:39.223198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:39.223198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From triangulated categories to module categories via homotopical algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Yann Palu","submitted_at":"2014-12-23T08:52:50Z","abstract_excerpt":"The category of modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category C has been given two different descriptions: On the one hand, as shown by Osamu Iyama and Yuji Yoshino, it is equivalent to an ideal quotient of a subcategory of C. On the other hand, Aslak Buan and Robert Marsh proved that this module category is also equivalent to some localisation of C. In this paper, we give a conceptual interpretation, inspired from homotopical algebra, of this double description. Our main aim, yet to be acheived, is to generalise Buan-Marsh's result to the case o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7289","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":"1412.7289","created_at":"2026-05-18T02:30:39.223257+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.7289v1","created_at":"2026-05-18T02:30:39.223257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7289","created_at":"2026-05-18T02:30:39.223257+00:00"},{"alias_kind":"pith_short_12","alias_value":"T42KFLZGTJJE","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"T42KFLZGTJJER57F","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"T42KFLZG","created_at":"2026-05-18T12:28:49.207871+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/T42KFLZGTJJER57F3TWXIP62N2","json":"https://pith.science/pith/T42KFLZGTJJER57F3TWXIP62N2.json","graph_json":"https://pith.science/api/pith-number/T42KFLZGTJJER57F3TWXIP62N2/graph.json","events_json":"https://pith.science/api/pith-number/T42KFLZGTJJER57F3TWXIP62N2/events.json","paper":"https://pith.science/paper/T42KFLZG"},"agent_actions":{"view_html":"https://pith.science/pith/T42KFLZGTJJER57F3TWXIP62N2","download_json":"https://pith.science/pith/T42KFLZGTJJER57F3TWXIP62N2.json","view_paper":"https://pith.science/paper/T42KFLZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.7289&json=true","fetch_graph":"https://pith.science/api/pith-number/T42KFLZGTJJER57F3TWXIP62N2/graph.json","fetch_events":"https://pith.science/api/pith-number/T42KFLZGTJJER57F3TWXIP62N2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T42KFLZGTJJER57F3TWXIP62N2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T42KFLZGTJJER57F3TWXIP62N2/action/storage_attestation","attest_author":"https://pith.science/pith/T42KFLZGTJJER57F3TWXIP62N2/action/author_attestation","sign_citation":"https://pith.science/pith/T42KFLZGTJJER57F3TWXIP62N2/action/citation_signature","submit_replication":"https://pith.science/pith/T42KFLZGTJJER57F3TWXIP62N2/action/replication_record"}},"created_at":"2026-05-18T02:30:39.223257+00:00","updated_at":"2026-05-18T02:30:39.223257+00:00"}