{"paper":{"title":"Kan injectivity in order-enriched categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LO","authors_text":"Jiri Adamek, Jiri Velebil, Lurdes Sousa","submitted_at":"2013-11-07T15:56:20Z","abstract_excerpt":"Continuous lattices were characterised by Martin Escardo as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general categories enriched in posets. For every class H of morphisms we study the subcategory of all objects Kan-injective w.r.t. H and all morphisms preserving Kan-extensions. For categories such as Top_0 and Pos we prove that whenever H is a set of morphisms, the above subcategory is monadic, and the monad it creates is a Kock-Zoeberlein monad. However, this does not generalise to proper classes: we present a class of conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1721","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"}