{"paper":{"title":"On monoids in the category of sets and relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Anna Jen\\v{c}ov\\'a, Gejza Jen\\v{c}a","submitted_at":"2017-03-10T15:50:48Z","abstract_excerpt":"The category $\\mathbf{Rel}$ is the category of sets (objects) and relations (morphisms). Equipped with the direct product of sets, $\\mathbf{Rel}$ is a monoidal category. Moreover, $\\mathbf{Rel}$ is a locally posetal 2-category, since every homset $\\mathbf{Rel}(A,B)$ is a poset with respect to inclusion. We examine the 2-category of monoids $\\mathbf{RelMon}$ in this category. The morphism we use are lax.\n  This category includes, as subcategories, various interesting classes: hypergroups, partial monoids (which include various types of quantum logics, for example effect algebras) and small cate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03728","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"}