Coproducts of Distributive Lattice based Algebras | Zendy

Leonardo Manuel Cabrer | Zendy; H. A. Priestley | Zendy

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Coproducts 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) , duality (order theory) , constructive , functor , pure mathematics , constraint satisfaction problem , lattice (music) , topological space , algebra over a field , computer science , discrete mathematics , process (computing) , programming language , statistics , physics , probabilistic logic , acoustics

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.

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