{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:A22XFHD3NZVRRRUQO3E5ENXC6I","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":"e7bb21926be58e20a7c4669d90cce7808e6a28945a296410f390017788059fbb","cross_cats_sorted":["math.CT","math.RT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-09-01T18:12:22Z","title_canon_sha256":"c6e5e183cdcd9aede7741c5f87c934e7d62674fdb767a1c68e26c6be9c4c6641"},"schema_version":"1.0","source":{"id":"2409.00793","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.00793","created_at":"2026-07-05T09:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"2409.00793v2","created_at":"2026-07-05T09:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.00793","created_at":"2026-07-05T09:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"A22XFHD3NZVR","created_at":"2026-07-05T09:41:01Z"},{"alias_kind":"pith_short_16","alias_value":"A22XFHD3NZVRRRUQ","created_at":"2026-07-05T09:41:01Z"},{"alias_kind":"pith_short_8","alias_value":"A22XFHD3","created_at":"2026-07-05T09:41:01Z"}],"graph_snapshots":[{"event_id":"sha256:3c9298045d3b2a7411bc07d525a4b907b6a61335e1432ac6b13d07264475e2ee","target":"graph","created_at":"2026-07-05T09:41:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.00793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By building on the notions of internal projective and injective objects in a module category introduced by Douglas, Schommer-Pries, and Snyder, we extend the reconstruction theory for module categories of Etingof and Ostrik. More explicitly, instead of algebra objects in finite tensor categories, we consider quasi-finite coalgebra objects in locally finite tensor categories. Moreover, we show that module categories over non-rigid monoidal categories can be reconstructed via lax module monads, which generalize algebra objects. For the monoidal category of finite-dimensional comodules over a (no","authors_text":"Mateusz Stroi\\'nski, Tony Zorman","cross_cats":["math.CT","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-09-01T18:12:22Z","title":"Reconstruction of module categories in the infinite and non-rigid settings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.00793","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":"sha256:08b96c2814803ee31003517a10beb1ae4223f63c7f22ce57bbe0c6af71b3319a","target":"record","created_at":"2026-07-05T09:41:01Z","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":"e7bb21926be58e20a7c4669d90cce7808e6a28945a296410f390017788059fbb","cross_cats_sorted":["math.CT","math.RT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-09-01T18:12:22Z","title_canon_sha256":"c6e5e183cdcd9aede7741c5f87c934e7d62674fdb767a1c68e26c6be9c4c6641"},"schema_version":"1.0","source":{"id":"2409.00793","kind":"arxiv","version":2}},"canonical_sha256":"06b5729c7b6e6b18c69076c9d236e2f21fbad3b0a5f5ccb764b12969605b519b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06b5729c7b6e6b18c69076c9d236e2f21fbad3b0a5f5ccb764b12969605b519b","first_computed_at":"2026-07-05T09:41:01.562674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:01.562674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c78ad9mtVGGRLbwTSvLJsqfm6DpLjy+CCOaN2M9pqndv8H2WtRzmZGEeWHUGOYcdkTQQKGNnYeHOIRrg+dYcBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:01.563142Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.00793","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08b96c2814803ee31003517a10beb1ae4223f63c7f22ce57bbe0c6af71b3319a","sha256:3c9298045d3b2a7411bc07d525a4b907b6a61335e1432ac6b13d07264475e2ee"],"state_sha256":"52a052dbadfe37c7520ceceecb5664f92ced3585ad152d79247754b50ce1f9f7"}