{"paper":{"title":"Generalized powerlocales via relation lifting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Jacob Vosmaer, Steve Vickers, Yde Venema","submitted_at":"2012-02-15T10:32:31Z","abstract_excerpt":"This paper introduces an endofunctor $\\VT$ on the category of frames, parametrized by an endofunctor $\\T$ on the category $\\Set$ that satisfies certain constraints. This generalizes Johnstone's construction of the Vietoris powerlocale, in the sense that his construction is obtained by taking for $\\T$ the finite covariant power set functor. Our construction of the $\\T$-powerlocale $\\VT \\bbL$ out of a frame $\\bbL$ is based on ideas from coalgebraic logic and makes explicit the connection between the Vietoris construction and Moss's coalgebraic cover modality.\n  We show how to extend certain natu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3264","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"}