{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WPYQVCHZI34IH3BMIHY57C4LJC","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":"c4a9f8d096743a3f3cbe7d2a9d111637b0e290acbab966e391b9565cbabc8c36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-12-12T14:38:10Z","title_canon_sha256":"891420945a71661f5410d0d25e3fdb1ee813ea8c1743899d8905e52a02f8d735"},"schema_version":"1.0","source":{"id":"1612.03711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03711","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03711v1","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03711","created_at":"2026-05-18T00:55:18Z"},{"alias_kind":"pith_short_12","alias_value":"WPYQVCHZI34I","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WPYQVCHZI34IH3BM","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WPYQVCHZ","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:9eeed1b108172e57221a521c104358c027fcf21b0282a03ec4f0f8eef6b249f3","target":"graph","created_at":"2026-05-18T00:55:18Z","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 introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are precisely the finite-injectivity classes. We prove a $2$-duality between the $2$-category of small exact categories and the $2$-category of definable categories, and provide a new proof of its additive version. We further introduce a third vertex of the $2$-category of regular toposes and show that the diagram of $2$-(anti-)equivalences between three $2$-categorie","authors_text":"Amit Kuber, Ji\\v{r}\\'i Rosick\\'y","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-12-12T14:38:10Z","title":"Definable Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03711","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":"sha256:6f9852cb9b4db8a505055e4625e8b9b291d64803477dadb20e2cae1bb25e479f","target":"record","created_at":"2026-05-18T00:55:18Z","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":"c4a9f8d096743a3f3cbe7d2a9d111637b0e290acbab966e391b9565cbabc8c36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-12-12T14:38:10Z","title_canon_sha256":"891420945a71661f5410d0d25e3fdb1ee813ea8c1743899d8905e52a02f8d735"},"schema_version":"1.0","source":{"id":"1612.03711","kind":"arxiv","version":1}},"canonical_sha256":"b3f10a88f946f883ec2c41f1df8b8b4888c924cc08cd39cfd95b456270d4dcdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3f10a88f946f883ec2c41f1df8b8b4888c924cc08cd39cfd95b456270d4dcdd","first_computed_at":"2026-05-18T00:55:18.509122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:18.509122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lTK6mXR+DuE+Qf5LOrvw/XEWm/NkhuHfYl5zjUHRaM4w1iu8t4tR7/RoO/7DSRbEab8J5jyWL94MizA+amzqBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:18.509768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f9852cb9b4db8a505055e4625e8b9b291d64803477dadb20e2cae1bb25e479f","sha256:9eeed1b108172e57221a521c104358c027fcf21b0282a03ec4f0f8eef6b249f3"],"state_sha256":"5ab2c7787f036ffff36d437112c64f15d15bdc2a2d449b7a8bbcf4528794f787"}