A connection between finite-to-finite universal and Q-universal quasivarieties
by
M.E. Adams
State University of New York at New Paltz
Coauthors: W. Dziobiak (University of Puerto Rico at Mayaguez)

Let K be a quasivariety of algebraic systems of finite type. K is said to be universal if the category G of all directed graphs is isomorphic to a full subcategory of K. If an embedding of G may be effected by a functor F:G --> K which assigns a finite algebraic system to each finite graph, then K is said to be finite-to-finite universal. K is said to be Q-universal if, for any quasivariety M of finite type, L(M) is a homomorphic image of a sublattice of L(K), where L(M) and L(K) are the lattices of quasivarieties contained in M and K, respectively.

We establish a connection between these two, apparently unrelated, notions by showing that, if K is finite-to-finite universal due to a functor F such that, for all finite G and H, the morphism F(f):F(G) --> F(H) is onto in K whenever f:G --> H is a strong morphism in G, then K is Q-universal. Using this connection a number of quasivarieties are shown to be Q-universal.

Date received: April 30, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-21.