Abstract.
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 \( \longrightarrow \) 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, then K is Q-universal. Using this connection a number of quasivarieties are shown to be Q-universal.
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Received February 8, 2000; accepted in final form December 23, 2000.
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Adams, M., Dziobiak, W. Finite-to-finite universal quasivarieties are Q-universal. Algebra univers. 46, 253–283 (2001). https://doi.org/10.1007/PL00000343
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DOI: https://doi.org/10.1007/PL00000343