{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:SCMV72VWENQWEMLOF3XDINRUHY","short_pith_number":"pith:SCMV72VW","schema_version":"1.0","canonical_sha256":"90995feab6236162316e2eee3436343e2f1f08bc8bbb181ae5958227e3488d7e","source":{"kind":"arxiv","id":"1309.6039","version":5},"attestation_state":"computed","paper":{"title":"Derived categories of $N$-complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CT","authors_text":"Jun-ichi Miyachi, Kiriko Kato, Osamu Iyama","submitted_at":"2013-09-24T03:46:23Z","abstract_excerpt":"We study the homotopy category $\\mathsf{K}_{N}(\\mathcal{B})$ of $N$-complexes of an additive category $\\mathcal{B}$ and the derived category $\\mathsf{D}_{N}(\\mathcal{A})$ of an abelian category $\\mathcal{A}$. First we show that both $\\mathsf{K}_N(\\mathcal{B})$ and $\\mathsf{D}_N(\\mathcal{A})$ have natural structures of triangulated categories. Then we establish a theory of projective (resp., injective) resolutions and derived functors. Finally, under some conditions of an abelian category $\\mathcal{A}$, we show that $\\mathsf{D}_{N}(\\mathcal{A})$ is triangle equivalent to the ordinary derived ca"},"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":"1309.6039","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-09-24T03:46:23Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"61f5c309e1cc96af6973a20e7ef7ee048a46cbd88066960e51bf93ff939fb90d","abstract_canon_sha256":"2d7d4f4ced50711b2e248033504e32305df79a5a74243cf76edda62fe20d02ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:55.989991Z","signature_b64":"H4w5uc/z5Fb72+IL78TNIjPdsVcfNzM7go+6goanfH5kG7lDZTlrJpSNhAJ5088YIrlOOVKi6W5oLf5NCMmrDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90995feab6236162316e2eee3436343e2f1f08bc8bbb181ae5958227e3488d7e","last_reissued_at":"2026-05-18T00:29:55.989564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:55.989564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derived categories of $N$-complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CT","authors_text":"Jun-ichi Miyachi, Kiriko Kato, Osamu Iyama","submitted_at":"2013-09-24T03:46:23Z","abstract_excerpt":"We study the homotopy category $\\mathsf{K}_{N}(\\mathcal{B})$ of $N$-complexes of an additive category $\\mathcal{B}$ and the derived category $\\mathsf{D}_{N}(\\mathcal{A})$ of an abelian category $\\mathcal{A}$. First we show that both $\\mathsf{K}_N(\\mathcal{B})$ and $\\mathsf{D}_N(\\mathcal{A})$ have natural structures of triangulated categories. Then we establish a theory of projective (resp., injective) resolutions and derived functors. Finally, under some conditions of an abelian category $\\mathcal{A}$, we show that $\\mathsf{D}_{N}(\\mathcal{A})$ is triangle equivalent to the ordinary derived ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6039","kind":"arxiv","version":5},"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":"1309.6039","created_at":"2026-05-18T00:29:55.989626+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.6039v5","created_at":"2026-05-18T00:29:55.989626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6039","created_at":"2026-05-18T00:29:55.989626+00:00"},{"alias_kind":"pith_short_12","alias_value":"SCMV72VWENQW","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SCMV72VWENQWEMLO","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SCMV72VW","created_at":"2026-05-18T12:27:59.945178+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/SCMV72VWENQWEMLOF3XDINRUHY","json":"https://pith.science/pith/SCMV72VWENQWEMLOF3XDINRUHY.json","graph_json":"https://pith.science/api/pith-number/SCMV72VWENQWEMLOF3XDINRUHY/graph.json","events_json":"https://pith.science/api/pith-number/SCMV72VWENQWEMLOF3XDINRUHY/events.json","paper":"https://pith.science/paper/SCMV72VW"},"agent_actions":{"view_html":"https://pith.science/pith/SCMV72VWENQWEMLOF3XDINRUHY","download_json":"https://pith.science/pith/SCMV72VWENQWEMLOF3XDINRUHY.json","view_paper":"https://pith.science/paper/SCMV72VW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.6039&json=true","fetch_graph":"https://pith.science/api/pith-number/SCMV72VWENQWEMLOF3XDINRUHY/graph.json","fetch_events":"https://pith.science/api/pith-number/SCMV72VWENQWEMLOF3XDINRUHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SCMV72VWENQWEMLOF3XDINRUHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SCMV72VWENQWEMLOF3XDINRUHY/action/storage_attestation","attest_author":"https://pith.science/pith/SCMV72VWENQWEMLOF3XDINRUHY/action/author_attestation","sign_citation":"https://pith.science/pith/SCMV72VWENQWEMLOF3XDINRUHY/action/citation_signature","submit_replication":"https://pith.science/pith/SCMV72VWENQWEMLOF3XDINRUHY/action/replication_record"}},"created_at":"2026-05-18T00:29:55.989626+00:00","updated_at":"2026-05-18T00:29:55.989626+00:00"}