{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2XSXOKZL6CJRZJLWJUXN7UCLHF","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":"398a58c0f9e26475a2f365ebb3ef994710e4dedcc667d6f4ca89ea25b3be1b99","cross_cats_sorted":["math.AT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-09-26T16:07:42Z","title_canon_sha256":"37becbd2e644c41cddb3bf6e42e383fbd0c93a362c4b8b311649e14e780f5818"},"schema_version":"1.0","source":{"id":"1309.6952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6952","created_at":"2026-05-18T03:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6952v1","created_at":"2026-05-18T03:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6952","created_at":"2026-05-18T03:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"2XSXOKZL6CJR","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2XSXOKZL6CJRZJLW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2XSXOKZL","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:0cf951dd4c901a1227bf1ac996ab7c2539d46438a38706eb751b5dbb2f5668b7","target":"graph","created_at":"2026-05-18T03:12:09Z","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":"We prove that the category of dg-coalgebras is symmetric monoidal closed and that the category of dg-algebras is enriched, tensored, cotensored and strongly monoidal over that of coalgebras. We apply this formalism to reconstruct several known adjunctions, notably the bar-cobar adjunction.","authors_text":"Andr\\'e Joyal, Matthieu Anel","cross_cats":["math.AT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-09-26T16:07:42Z","title":"Sweedler Theory for (co)algebras and the bar-cobar constructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6952","kind":"arxiv","version":1},"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:d2a925cd8616ead19f5eb17058a5a21e888150e7d9e0aa530bb04ff26fce96c9","target":"record","created_at":"2026-05-18T03:12:09Z","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":"398a58c0f9e26475a2f365ebb3ef994710e4dedcc667d6f4ca89ea25b3be1b99","cross_cats_sorted":["math.AT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-09-26T16:07:42Z","title_canon_sha256":"37becbd2e644c41cddb3bf6e42e383fbd0c93a362c4b8b311649e14e780f5818"},"schema_version":"1.0","source":{"id":"1309.6952","kind":"arxiv","version":1}},"canonical_sha256":"d5e5772b2bf0931ca5764d2edfd04b397668b74d6dfdf903fef51cd0ea4b9664","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5e5772b2bf0931ca5764d2edfd04b397668b74d6dfdf903fef51cd0ea4b9664","first_computed_at":"2026-05-18T03:12:09.644605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:09.644605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7vMysGVLlncMbE0WSs892tMILPCvMoJTyz698J9aais9+n4eZj6EoEyxNUjlLY5PBLvtwidL374SPCLYYvkoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:09.645358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2a925cd8616ead19f5eb17058a5a21e888150e7d9e0aa530bb04ff26fce96c9","sha256:0cf951dd4c901a1227bf1ac996ab7c2539d46438a38706eb751b5dbb2f5668b7"],"state_sha256":"72c3e459b0c24536f0817f7104867c4588708866f55f7f1862f3c3994124fa7e"}