{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:75AQ4Y6JKW4N5A2MHD4KLL3EUO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"61adaccd9663e401ae384322af2dd1e06043c032b969b1cccd7a4660c588ae08","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-07T19:09:48Z","title_canon_sha256":"4af79515fd76323ad863d4aeb813b4df274f856918ea0bb345036880412ef039"},"schema_version":"1.0","source":{"id":"1312.2127","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2127","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2127v2","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2127","created_at":"2026-05-18T00:51:19Z"},{"alias_kind":"pith_short_12","alias_value":"75AQ4Y6JKW4N","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"75AQ4Y6JKW4N5A2M","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"75AQ4Y6J","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:80da977733be3604c54ead9589489643129b2d9fd0944698252c20940340c975","target":"graph","created_at":"2026-05-18T00:51:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we introduce a functor, called the simplicial nerve of an A-infinity category, defined on the category of (small) A-infinity categories with values in simplicial sets. We prove that the simplicial nerve of any A-infinity category is an infinity category. This construction extends functorially the nerve construction for differential graded categories proposed by J.Lurie in Higher Algebra. We prove that if a differential graded category is pretriangulated in the sense of A.I.Bondal-M.Kapranov, then its nerve is a stable infinity category in the sense of J.Lurie.","authors_text":"Giovanni Faonte","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-07T19:09:48Z","title":"Simplicial nerve of an A-infinity category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2127","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4a02a7e6e57013fabb00c186015f3832ac22579168d87023134d2b56cd410ae2","target":"record","created_at":"2026-05-18T00:51:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"61adaccd9663e401ae384322af2dd1e06043c032b969b1cccd7a4660c588ae08","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-07T19:09:48Z","title_canon_sha256":"4af79515fd76323ad863d4aeb813b4df274f856918ea0bb345036880412ef039"},"schema_version":"1.0","source":{"id":"1312.2127","kind":"arxiv","version":2}},"canonical_sha256":"ff410e63c955b8de834c38f8a5af64a3a860e36460351e7e11bcc284b2d8a403","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff410e63c955b8de834c38f8a5af64a3a860e36460351e7e11bcc284b2d8a403","first_computed_at":"2026-05-18T00:51:19.304675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:19.304675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vr4yDVMli338zT7t0foeeGtP9VamrWyCY8ehrgXMsNVFN7UXtpyKSukBQpm0297cgLpJfV1eITG3Ev1S96kNAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:19.305426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2127","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a02a7e6e57013fabb00c186015f3832ac22579168d87023134d2b56cd410ae2","sha256:80da977733be3604c54ead9589489643129b2d9fd0944698252c20940340c975"],"state_sha256":"fc1cdcb1d0cb004676ccca02c9c2cd95f39b5386318d0347bb2ced4b3acf1dee"}