Open AccessCoproducts of Distributive Lattice based Algebras
Author(s) -
Leonardo Manuel Cabrer,
H. A. Priestley
Publication year - 2018
Publication title -
epic series in computing
Language(s) - English
Resource type - Conference proceedings
ISSN - 2398-7340
DOI - 10.29007/vx1v
Subject(s) - coproduct , distributive property , mathematics , cartesian product , variety (cybernetics) , functor , duality (order theory) , constructive , lattice (music) , pure mathematics , constraint satisfaction problem , algebra over a field , topological space , computer science , discrete mathematics , programming language , physics , acoustics , statistics , process (computing) , probabilistic logic
The analysis of coproducts in varieties of algebras has generally been variety-specific, relying on tools tailored to particular classes of algebras. A recurring theme, however, is the use of a categorical duality. Among the dualities and topological representations in the literature, natural dualities are particularly well behaved with respect to coproduct. Since (multisorted) natural dualities are based on hom-functors, they send coproducts into cartesian products. We carry out a systematic study of coproducts for finitely generated quasivarieties A that admit a (term) reduct in the variety D of bounded distributive lattices.