{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VJW3XCNISVKVRMYTIIR6UJG4QB","short_pith_number":"pith:VJW3XCNI","schema_version":"1.0","canonical_sha256":"aa6dbb89a8955558b3134223ea24dc806e55c64e87aa3be83c4eca711bc409d1","source":{"kind":"arxiv","id":"2504.16690","version":2},"attestation_state":"computed","paper":{"title":"Logic and Concepts in the 2-category of Topoi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.CT"],"primary_cat":"math.LO","authors_text":"Ivan Di Liberti, Lingyuan Ye","submitted_at":"2025-04-23T13:21:57Z","abstract_excerpt":"We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the formal theory of Kan extension in this 2-category (pointwise Kan extensions, fully faithful morphisms, etc.). We use this technology to introduce fragments of geometric logic, and we accommodate essentially algebraic, disjunctive, regular, and coherent logic in our framework, together with some more exotic examples. We show that each fragment $\\mathcal{H}$ in our sense identifies a lax-idempotent (relative) pseudomon"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2504.16690","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-04-23T13:21:57Z","cross_cats_sorted":["cs.LO","math.CT"],"title_canon_sha256":"1df424f40110a25854810f1f7f751959398b1b4d378ad6aa8c4bb22ffcd366b7","abstract_canon_sha256":"c1c1f64e46f01397c7c8b7ac5352b067049bd73eb66bf9d79eb47659524b9d59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:30.904368Z","signature_b64":"tf5WXqGqmoQUTwdD/YH4ZHFTJsh2YN/XZcH/ZNa6LDPVWUjAgIKBvjBFEn0Sb9gsGTva8Vk+O2LYvpkpoJj7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa6dbb89a8955558b3134223ea24dc806e55c64e87aa3be83c4eca711bc409d1","last_reissued_at":"2026-07-05T11:06:30.903857Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:30.903857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logic and Concepts in the 2-category of Topoi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.CT"],"primary_cat":"math.LO","authors_text":"Ivan Di Liberti, Lingyuan Ye","submitted_at":"2025-04-23T13:21:57Z","abstract_excerpt":"We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the formal theory of Kan extension in this 2-category (pointwise Kan extensions, fully faithful morphisms, etc.). We use this technology to introduce fragments of geometric logic, and we accommodate essentially algebraic, disjunctive, regular, and coherent logic in our framework, together with some more exotic examples. We show that each fragment $\\mathcal{H}$ in our sense identifies a lax-idempotent (relative) pseudomon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16690","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.16690/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2504.16690","created_at":"2026-07-05T11:06:30.903914+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.16690v2","created_at":"2026-07-05T11:06:30.903914+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16690","created_at":"2026-07-05T11:06:30.903914+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJW3XCNISVKV","created_at":"2026-07-05T11:06:30.903914+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJW3XCNISVKVRMYT","created_at":"2026-07-05T11:06:30.903914+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJW3XCNI","created_at":"2026-07-05T11:06:30.903914+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.22071","citing_title":"Duality theory for categorical theories","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB","json":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB.json","graph_json":"https://pith.science/api/pith-number/VJW3XCNISVKVRMYTIIR6UJG4QB/graph.json","events_json":"https://pith.science/api/pith-number/VJW3XCNISVKVRMYTIIR6UJG4QB/events.json","paper":"https://pith.science/paper/VJW3XCNI"},"agent_actions":{"view_html":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB","download_json":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB.json","view_paper":"https://pith.science/paper/VJW3XCNI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.16690&json=true","fetch_graph":"https://pith.science/api/pith-number/VJW3XCNISVKVRMYTIIR6UJG4QB/graph.json","fetch_events":"https://pith.science/api/pith-number/VJW3XCNISVKVRMYTIIR6UJG4QB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB/action/storage_attestation","attest_author":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB/action/author_attestation","sign_citation":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB/action/citation_signature","submit_replication":"https://pith.science/pith/VJW3XCNISVKVRMYTIIR6UJG4QB/action/replication_record"}},"created_at":"2026-07-05T11:06:30.903914+00:00","updated_at":"2026-07-05T11:06:30.903914+00:00"}