{"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"}