Coalgebraic representations of distributive lattices with operators |
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Authors: | M.M. Bonsangue A. Kurz I.M. Rewitzky |
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Affiliation: | a LIACS, Leiden University, The Netherlands b University of Leicester, United Kingdom c University of Stellenbosch, South Africa |
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Abstract: | We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators. |
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Keywords: | 06D05 06D50 18C10 03C05 03G10 |
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