{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NWB44BXK4BK5EXOS3T742W3BJM","short_pith_number":"pith:NWB44BXK","schema_version":"1.0","canonical_sha256":"6d83ce06eae055d25dd2dcffcd5b614b183f9949632924026bba3b7d5f301a3e","source":{"kind":"arxiv","id":"1105.6206","version":2},"attestation_state":"computed","paper":{"title":"Double Adjunctions and Free Monads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Joachim Kock, Nicola Gambino, Thomas M. Fiore","submitted_at":"2011-05-31T08:57:01Z","abstract_excerpt":"We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg--Moore objects in double categories. We improve upon our earlier result in \"Monads in Double Categories\", JPAA 215:6, pages 1174-1197, 2011, to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category. We also prove that a double category admits Eilenberg--Moore objects if and only if a certain parameterized presheaf i"},"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":"1105.6206","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2011-05-31T08:57:01Z","cross_cats_sorted":[],"title_canon_sha256":"ae54c7cb82ba7ebbafb6e60d2aef133aa200fda6cfc793909353759da6d0d2af","abstract_canon_sha256":"f4eaf0dac293e05d4ecc7d54bc0c53a74003b8e4d8a8fefe811dc7a8d83e3af2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:51.354977Z","signature_b64":"T1wvRq2twofI6ykcBRzxppR2d6enl1agxVZJNdyrZkkzxUBVoGW5U5YZ/EDLCeOO7+S66gLBQZE21PmO7DbYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d83ce06eae055d25dd2dcffcd5b614b183f9949632924026bba3b7d5f301a3e","last_reissued_at":"2026-05-18T02:47:51.354450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:51.354450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Double Adjunctions and Free Monads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Joachim Kock, Nicola Gambino, Thomas M. Fiore","submitted_at":"2011-05-31T08:57:01Z","abstract_excerpt":"We characterize double adjunctions in terms of presheaves and universal squares, and then apply these characterizations to free monads and Eilenberg--Moore objects in double categories. We improve upon our earlier result in \"Monads in Double Categories\", JPAA 215:6, pages 1174-1197, 2011, to conclude: if a double category with cofolding admits the construction of free monads in its horizontal 2-category, then it also admits the construction of free monads as a double category. We also prove that a double category admits Eilenberg--Moore objects if and only if a certain parameterized presheaf i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6206","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":""},"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":"1105.6206","created_at":"2026-05-18T02:47:51.354513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.6206v2","created_at":"2026-05-18T02:47:51.354513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6206","created_at":"2026-05-18T02:47:51.354513+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWB44BXK4BK5","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWB44BXK4BK5EXOS","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWB44BXK","created_at":"2026-05-18T12:26:37.096874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM","json":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM.json","graph_json":"https://pith.science/api/pith-number/NWB44BXK4BK5EXOS3T742W3BJM/graph.json","events_json":"https://pith.science/api/pith-number/NWB44BXK4BK5EXOS3T742W3BJM/events.json","paper":"https://pith.science/paper/NWB44BXK"},"agent_actions":{"view_html":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM","download_json":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM.json","view_paper":"https://pith.science/paper/NWB44BXK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.6206&json=true","fetch_graph":"https://pith.science/api/pith-number/NWB44BXK4BK5EXOS3T742W3BJM/graph.json","fetch_events":"https://pith.science/api/pith-number/NWB44BXK4BK5EXOS3T742W3BJM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM/action/storage_attestation","attest_author":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM/action/author_attestation","sign_citation":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM/action/citation_signature","submit_replication":"https://pith.science/pith/NWB44BXK4BK5EXOS3T742W3BJM/action/replication_record"}},"created_at":"2026-05-18T02:47:51.354513+00:00","updated_at":"2026-05-18T02:47:51.354513+00:00"}