{"paper":{"title":"Monads on Q-Cat and their lax extensions to Q-Dist","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Hongliang Lai, Walter Tholen","submitted_at":"2016-09-11T21:00:47Z","abstract_excerpt":"For a small quantaloid $\\mathcal{Q}$, we consider 2-monads on the 2-category $\\mathcal{Q}$-$\\bf{Cat}$ and their lax extensions to the 2-category $\\mathcal{Q}$-$\\bf{Dist}$ of small $\\mathcal{Q}$-categories and their distributors, in particular those lax extensions that are flat, in the sense that they map identity distributors to identity distributors. In fact, unlike in the discrete case, a 2-monad on $\\mathcal{Q}$-$\\bf{Cat}$ may admit only one flat lax extension. Every ordinary monad on the comma category $\\bf{Set}/{\\rm ob}\\mathcal{Q}$ with a lax extension to $\\mathcal{Q}$-$\\bf{Rel}$ gives ri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03214","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":""},"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"}