Almost ff-universality Implies Q-universality

摘要

A concrete category mathbb Qmathbb {Q} is finite-to-finite (algebraically) almost universal if the category of graphs and graph homomorphisms can be embedded into mathbb Qmathbb {Q} in such a way that finite mathbb Qmathbb {Q}-objects are assigned to finite graphs and non-constant mathbb Qmathbb {Q}-morphisms between any mathbb Qmathbb {Q}-objects assigned to graphs are exactly those arising from graph homomorphisms. A quasivariety mathbb Qmathbb {Q} of algebraic systems of a finite similarity type is Q-universal if the lattice of all subquasivarieties of any quasivariety mathbb Rmathbb {R} of algebraic systems of a finite similarity type is isomorphic to a quotient lattice of a sublattice of the subquasivariety lattice of mathbb Qmathbb {Q}. This paper shows that any finite-to-finite (algebraically) almost universal quasivariety mathbb Qmathbb {Q} of a finite type is Q-universal.