2014/03/30 by Gábor Czédli, Czédli, Gábor
Computer Science · Decision Sciences · Mathematics · #06B10 #Advanced Algebra and Logic #Bounded function #Combinatorics #Congruence (geometry) #Congruence relation #Converse #Discrete mathematics #FOS: Mathematics #Fuzzy and Soft Set Theory #Geometry #Lattice (music) #Mathematical analysis #Mathematics #Monotone polygon #Morphism #Pure mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #math.RA #msc:06B10
paper · pdf · doi:10.48550/arxiv.1403.7821
6 pages, no figure
openalex publication_date 2014/03/30 · arxiv created 2014/09/05 · arxiv updated 2014/09/08 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
For a lattice L with 0 and 1, let Princ L denote the ordered set of principal\ncongruences of L. For 0,1-sublattices A subseteq B of L, congruence\ngeneration defines a natural map from Princ A to Princ B. In this way, we\nobtain a small category of bounded ordered sets as objects and some\n0-separating 0,1-preserving monotone maps as morphisms such that every\nhom-set consists of at most one morphism. We prove the converse: each small\ncategory of bounded ordered set with these properties is representable by\nprincipal lattice congruences in the above sense.\n