{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:SUNEHXRZWVVSD6R76VH2KVYW3W","short_pith_number":"pith:SUNEHXRZ","schema_version":"1.0","canonical_sha256":"951a43de39b56b21fa3ff54fa55716dd80a95f361f185595dac330f6ac5a32a5","source":{"kind":"arxiv","id":"2410.11728","version":1},"attestation_state":"computed","paper":{"title":"Logical Structure on Inverse Functor Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.LO"],"primary_cat":"math.CT","authors_text":"Chris Kapulkin, Marcelo Fiore, Yufeng Li","submitted_at":"2024-10-15T16:00:33Z","abstract_excerpt":"Inspired by recent work on the categorical semantics of dependent type theories, we investigate the following question: When is logical structure (crucially, dependent-product and subobject-classifier structure) induced from a category to categories of diagrams in it? Our work offers several answers, providing a variety of conditions on both the category itself and the indexing category of diagrams. Additionally, motivated by homotopical considerations, we investigate the case when the indexing category is equipped with a class of weak equivalences and study conditions under which the localiza"},"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":"2410.11728","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-10-15T16:00:33Z","cross_cats_sorted":["cs.LO","math.LO"],"title_canon_sha256":"9e644fb5cc16d3aef05950f89ef66188c2d73d9285ac4660e82bebf2646aa971","abstract_canon_sha256":"f3c7a81800bb4f982bf749f36093bfddc90e22d234c33bc73e35e17de6d9c278"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:20:58.088085Z","signature_b64":"Cz3ifPhFy9AVuaKxWn03AoguCWwvJVsvrv2Mjc73GMtjJhFng6jYKj05T4ghK7aprs/h54J/V53ogrlV+LXUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"951a43de39b56b21fa3ff54fa55716dd80a95f361f185595dac330f6ac5a32a5","last_reissued_at":"2026-07-05T09:20:58.087723Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:20:58.087723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logical Structure on Inverse Functor Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.LO"],"primary_cat":"math.CT","authors_text":"Chris Kapulkin, Marcelo Fiore, Yufeng Li","submitted_at":"2024-10-15T16:00:33Z","abstract_excerpt":"Inspired by recent work on the categorical semantics of dependent type theories, we investigate the following question: When is logical structure (crucially, dependent-product and subobject-classifier structure) induced from a category to categories of diagrams in it? Our work offers several answers, providing a variety of conditions on both the category itself and the indexing category of diagrams. Additionally, motivated by homotopical considerations, we investigate the case when the indexing category is equipped with a class of weak equivalences and study conditions under which the localiza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.11728","kind":"arxiv","version":1},"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/2410.11728/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":"2410.11728","created_at":"2026-07-05T09:20:58.087789+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.11728v1","created_at":"2026-07-05T09:20:58.087789+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.11728","created_at":"2026-07-05T09:20:58.087789+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUNEHXRZWVVS","created_at":"2026-07-05T09:20:58.087789+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUNEHXRZWVVSD6R7","created_at":"2026-07-05T09:20:58.087789+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUNEHXRZ","created_at":"2026-07-05T09:20:58.087789+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.04472","citing_title":"Pushforwards in Inverse Homotopical Diagrams","ref_index":2024,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W","json":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W.json","graph_json":"https://pith.science/api/pith-number/SUNEHXRZWVVSD6R76VH2KVYW3W/graph.json","events_json":"https://pith.science/api/pith-number/SUNEHXRZWVVSD6R76VH2KVYW3W/events.json","paper":"https://pith.science/paper/SUNEHXRZ"},"agent_actions":{"view_html":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W","download_json":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W.json","view_paper":"https://pith.science/paper/SUNEHXRZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.11728&json=true","fetch_graph":"https://pith.science/api/pith-number/SUNEHXRZWVVSD6R76VH2KVYW3W/graph.json","fetch_events":"https://pith.science/api/pith-number/SUNEHXRZWVVSD6R76VH2KVYW3W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W/action/storage_attestation","attest_author":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W/action/author_attestation","sign_citation":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W/action/citation_signature","submit_replication":"https://pith.science/pith/SUNEHXRZWVVSD6R76VH2KVYW3W/action/replication_record"}},"created_at":"2026-07-05T09:20:58.087789+00:00","updated_at":"2026-07-05T09:20:58.087789+00:00"}