{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:4MDI3U7XNAQABMZJ5SP55WTRKQ","short_pith_number":"pith:4MDI3U7X","schema_version":"1.0","canonical_sha256":"e3068dd3f7682000b329ec9fdeda7154038e7645ecceaf869c6b7cdca5ed5ab7","source":{"kind":"arxiv","id":"2111.15299","version":4},"attestation_state":"computed","paper":{"title":"Quasitoposes as elementary quotient completions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.LO","authors_text":"Fabio Pasquali, Giuseppe Rosolini, Maria Emilia Maietti","submitted_at":"2021-11-30T11:25:11Z","abstract_excerpt":"The elementary quotient completion of an elementary doctrine in the sense of Lawvere was introduced in previous work by the first and third authors. It generalises the exact completion of a category with finite products and weak equalisers. In this paper we characterise when an elementary quotient completion is a quasi-topos. We obtain as a corollary a complete characterisation of when an elementary quotient completions is an elementary topos. As a byproduct we determine also when the elementary quotient completion of a tripos is equivalent to the doctrine obtained via the tripos-to-topos cons"},"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":"2111.15299","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2021-11-30T11:25:11Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"1248164e621dcd73a7e47ae5b6c7e64b45b61e204504737a1e4e596dd9f73029","abstract_canon_sha256":"7ffd88136301b0adff2c090a8eaf91b1bef97026532f78c4ccfdc09a2e21f0b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:11:51.484218Z","signature_b64":"K2QvdMGYkH1VEYpwJfdpjqdZmHm9uiEHWrnzerFSk6tdePWdeHoQNcBGTB1rbh7rZz1rT6VB/1nOpa8FX+DZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3068dd3f7682000b329ec9fdeda7154038e7645ecceaf869c6b7cdca5ed5ab7","last_reissued_at":"2026-06-23T01:11:51.483665Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:11:51.483665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasitoposes as elementary quotient completions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.LO","authors_text":"Fabio Pasquali, Giuseppe Rosolini, Maria Emilia Maietti","submitted_at":"2021-11-30T11:25:11Z","abstract_excerpt":"The elementary quotient completion of an elementary doctrine in the sense of Lawvere was introduced in previous work by the first and third authors. It generalises the exact completion of a category with finite products and weak equalisers. In this paper we characterise when an elementary quotient completion is a quasi-topos. We obtain as a corollary a complete characterisation of when an elementary quotient completions is an elementary topos. As a byproduct we determine also when the elementary quotient completion of a tripos is equivalent to the doctrine obtained via the tripos-to-topos cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.15299","kind":"arxiv","version":4},"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/2111.15299/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":"2111.15299","created_at":"2026-06-23T01:11:51.483731+00:00"},{"alias_kind":"arxiv_version","alias_value":"2111.15299v4","created_at":"2026-06-23T01:11:51.483731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.15299","created_at":"2026-06-23T01:11:51.483731+00:00"},{"alias_kind":"pith_short_12","alias_value":"4MDI3U7XNAQA","created_at":"2026-06-23T01:11:51.483731+00:00"},{"alias_kind":"pith_short_16","alias_value":"4MDI3U7XNAQABMZJ","created_at":"2026-06-23T01:11:51.483731+00:00"},{"alias_kind":"pith_short_8","alias_value":"4MDI3U7X","created_at":"2026-06-23T01:11:51.483731+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.11295","citing_title":"The Relational Quotient Completion","ref_index":45,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ","json":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ.json","graph_json":"https://pith.science/api/pith-number/4MDI3U7XNAQABMZJ5SP55WTRKQ/graph.json","events_json":"https://pith.science/api/pith-number/4MDI3U7XNAQABMZJ5SP55WTRKQ/events.json","paper":"https://pith.science/paper/4MDI3U7X"},"agent_actions":{"view_html":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ","download_json":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ.json","view_paper":"https://pith.science/paper/4MDI3U7X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2111.15299&json=true","fetch_graph":"https://pith.science/api/pith-number/4MDI3U7XNAQABMZJ5SP55WTRKQ/graph.json","fetch_events":"https://pith.science/api/pith-number/4MDI3U7XNAQABMZJ5SP55WTRKQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ/action/storage_attestation","attest_author":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ/action/author_attestation","sign_citation":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ/action/citation_signature","submit_replication":"https://pith.science/pith/4MDI3U7XNAQABMZJ5SP55WTRKQ/action/replication_record"}},"created_at":"2026-06-23T01:11:51.483731+00:00","updated_at":"2026-06-23T01:11:51.483731+00:00"}