Almost \textit{ff}-universality implies \(Q\)-universality
type: Item
instance of: scholarly article
title: Almost \textit{ff}-universality implies \(Q\)-universality
zbMATH Open document ID: 1182.08006
author: Václav Koubek
author: Jiří Sichler
published in: Applied Categorical Structures
publication date: 2009-11-16T00:00:00Z
review text: A concrete category \(\mathbb Q\) is finite-to-finite (algebraically) almost universal if the category of graphs and graph homomorphisms can be embedded into \(\mathbb Q\) in such a way that finite \(\mathbb Q\)-objects are assigned to finite graphs and non-constant \(\mathbb Q\)-morphisms between any \(\mathbb Q\)-objects assigned to graphs are exactly those arising from graph homomorphisms. A quasivariety \(\mathbb Q\) of algebraic systems of a finite similarity type is \(Q\)-universal if the lattice of all subquasivarieties of any quasivariety \(\mathbb R\) of algebraic systems of a finite similarity type is isomorphic to a quotient lattice of a sublattice of the subquasivariety lattice of \(\mathbb Q\). The main result of the paper states that any finite-to-finite (algebraically) almost universal quasivariety \(\mathbb Q\) of a finite type is \(Q\)-universal.
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 18B15
zbMATH DE Number: 5633349
zbMATH Keywords: quasivariety
zbMATH Keywords: \(Q\)-universality
zbMATH Keywords: almost full embedding
zbMATH Keywords: almost \textit{ff}-alg-universality
MaRDI profile type: Publication
full work available at URL: s10485-007-9122-3
OpenAlex ID: W2073275935
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DOI: 10.1007/S10485-007-9122-3
description: scientific article; zbMATH DE number 5633349