{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QZCWFX6MQYCAC3UKCO64UDOZNV","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":"3d7e29e3eb35c2d7fd719cdccf31f4c9008ef6359728f7d316dc0a8412c810de","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-15T23:28:52Z","title_canon_sha256":"909d7ac48e559586b737f20f105a1f28921b6d0c75c8d2398b72a6044b3d1242"},"schema_version":"1.0","source":{"id":"1801.05065","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05065","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05065v3","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05065","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"pith_short_12","alias_value":"QZCWFX6MQYCA","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QZCWFX6MQYCAC3UK","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QZCWFX6M","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:c1aa1a1430e48ccbc12fd0e89c75a26f636a159271f14f360d4e6d64aa10d6cf","target":"graph","created_at":"2026-05-17T23:48:40Z","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 define a comonad cohomology of track categories and we show it is linked by a long exact sequence to its Dwyer-Kan-Smith cohomology . Under mild hypothesis on the track category, we show that its comonad cohomology coincides, up to dimension shift, with its Dwyer-Kan-Smith cohomology, therefore obtaining an algebraic formulation of the latter. We also specialize our results to the case where the track category is a $2$-groupoid.","authors_text":"David Blanc, Simona Paoli","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-15T23:28:52Z","title":"Comonad Cohomology of Track Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05065","kind":"arxiv","version":3},"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":"sha256:452fe4b1b06e794643f47bbf3a501934e99a11229fce4d608e0432c4db9bad92","target":"record","created_at":"2026-05-17T23:48:40Z","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":"3d7e29e3eb35c2d7fd719cdccf31f4c9008ef6359728f7d316dc0a8412c810de","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-01-15T23:28:52Z","title_canon_sha256":"909d7ac48e559586b737f20f105a1f28921b6d0c75c8d2398b72a6044b3d1242"},"schema_version":"1.0","source":{"id":"1801.05065","kind":"arxiv","version":3}},"canonical_sha256":"864562dfcc8604016e8a13bdca0dd96d5221ef968e51dac555b6e8a4eafb92b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"864562dfcc8604016e8a13bdca0dd96d5221ef968e51dac555b6e8a4eafb92b6","first_computed_at":"2026-05-17T23:48:40.756352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:40.756352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JEf8YhEZ/72u/jc/+EkXTfXdYTCZpIDW+bWdqeeLq+76GqnTnXiMo96YsHZr1YZ1Ac89LbnSlYBB249qvKs9AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:40.756971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.05065","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:452fe4b1b06e794643f47bbf3a501934e99a11229fce4d608e0432c4db9bad92","sha256:c1aa1a1430e48ccbc12fd0e89c75a26f636a159271f14f360d4e6d64aa10d6cf"],"state_sha256":"3833df94b9b09114e178fc582159e93c5c7907e78b4e40370c2c20206f6e54f4"}