{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AR7B64UUGOZ4GNLVG5KK3XIPUA","short_pith_number":"pith:AR7B64UU","schema_version":"1.0","canonical_sha256":"047e1f729433b3c335753754addd0fa00ccfded02838f35ba369e4cf13794a6c","source":{"kind":"arxiv","id":"1605.04489","version":2},"attestation_state":"computed","paper":{"title":"Lax distributive laws for topology, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CT","authors_text":"Hongliang Lai, Lili Shen, Walter Tholen","submitted_at":"2016-05-15T02:00:17Z","abstract_excerpt":"For a small quantaloid $\\mathcal{Q}$ we consider four fundamental 2-monads $\\mathbb{T}$ on $\\mathcal{Q}\\text{-}{\\bf Cat}$, given by the presheaf 2-monad $\\mathbb{P}$ and the copresheaf 2-monad $\\mathbb{P}^{\\dagger}$, as well as by their two composite 2-monads, and establish that they all laxly distribute over $\\mathbb{P}$. These four 2-monads therefore admit lax extensions to the category $\\mathcal{Q}\\text{-}{\\bf Dist}$ of $\\mathcal{Q}$-categories and their distributors. We characterize the corresponding $(\\mathbb{T},\\mathcal{Q})$-categories in each of the four cases, leading us to both known "},"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":"1605.04489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-05-15T02:00:17Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3711357085b604db23a02121e032c583bbe4cffd8bd8fe05dfa9093841823d7c","abstract_canon_sha256":"bc8fee2c32f95851b860418210a1ec4c4c6cba87e144f8918fa1038d446e6301"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:28.841980Z","signature_b64":"6Wyqdy3CkYFJgK8+Zaqss/Qnwn7T2L1DwZJIPeDTCBh3jYC5ez+W/Wzmh7VKpQ0ZzJocHdKmUg9em8z8QVLNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"047e1f729433b3c335753754addd0fa00ccfded02838f35ba369e4cf13794a6c","last_reissued_at":"2026-05-18T00:40:28.841550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:28.841550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lax distributive laws for topology, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CT","authors_text":"Hongliang Lai, Lili Shen, Walter Tholen","submitted_at":"2016-05-15T02:00:17Z","abstract_excerpt":"For a small quantaloid $\\mathcal{Q}$ we consider four fundamental 2-monads $\\mathbb{T}$ on $\\mathcal{Q}\\text{-}{\\bf Cat}$, given by the presheaf 2-monad $\\mathbb{P}$ and the copresheaf 2-monad $\\mathbb{P}^{\\dagger}$, as well as by their two composite 2-monads, and establish that they all laxly distribute over $\\mathbb{P}$. These four 2-monads therefore admit lax extensions to the category $\\mathcal{Q}\\text{-}{\\bf Dist}$ of $\\mathcal{Q}$-categories and their distributors. We characterize the corresponding $(\\mathbb{T},\\mathcal{Q})$-categories in each of the four cases, leading us to both known "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04489","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":"1605.04489","created_at":"2026-05-18T00:40:28.841619+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.04489v2","created_at":"2026-05-18T00:40:28.841619+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04489","created_at":"2026-05-18T00:40:28.841619+00:00"},{"alias_kind":"pith_short_12","alias_value":"AR7B64UUGOZ4","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AR7B64UUGOZ4GNLV","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AR7B64UU","created_at":"2026-05-18T12:30:07.202191+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/AR7B64UUGOZ4GNLVG5KK3XIPUA","json":"https://pith.science/pith/AR7B64UUGOZ4GNLVG5KK3XIPUA.json","graph_json":"https://pith.science/api/pith-number/AR7B64UUGOZ4GNLVG5KK3XIPUA/graph.json","events_json":"https://pith.science/api/pith-number/AR7B64UUGOZ4GNLVG5KK3XIPUA/events.json","paper":"https://pith.science/paper/AR7B64UU"},"agent_actions":{"view_html":"https://pith.science/pith/AR7B64UUGOZ4GNLVG5KK3XIPUA","download_json":"https://pith.science/pith/AR7B64UUGOZ4GNLVG5KK3XIPUA.json","view_paper":"https://pith.science/paper/AR7B64UU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.04489&json=true","fetch_graph":"https://pith.science/api/pith-number/AR7B64UUGOZ4GNLVG5KK3XIPUA/graph.json","fetch_events":"https://pith.science/api/pith-number/AR7B64UUGOZ4GNLVG5KK3XIPUA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AR7B64UUGOZ4GNLVG5KK3XIPUA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AR7B64UUGOZ4GNLVG5KK3XIPUA/action/storage_attestation","attest_author":"https://pith.science/pith/AR7B64UUGOZ4GNLVG5KK3XIPUA/action/author_attestation","sign_citation":"https://pith.science/pith/AR7B64UUGOZ4GNLVG5KK3XIPUA/action/citation_signature","submit_replication":"https://pith.science/pith/AR7B64UUGOZ4GNLVG5KK3XIPUA/action/replication_record"}},"created_at":"2026-05-18T00:40:28.841619+00:00","updated_at":"2026-05-18T00:40:28.841619+00:00"}