Dualities for Subresiduated latttices

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A subresiduated lattice is a pair (A,D), where A is a bounded distributive lattice, D is a bounded sublattice of A and for every a, b ∈ A there is c ∈ D such that for all d ∈ D, d ∧ a ≤ b if and only if d ≤ c. This c is denoted by a → b. This pair can be regarded as an algebra ⟨A, ∧, ∨,→, 0, 1⟩ of type (2, 2, 2, 0, 0) where D = {a ∈ A : 1 → a = a}. The class of subresiduated lattices is a variety which properly contains to the variety of Heyting algebras. In this paper we present dual equivalences for the algebraic category of subresiduated lattices. More precisely, we develop a spectral style duality and a bitopological style duality for this algebraic category. Finally we study the connections of these results with a known Priestley style duality for the algebraic category of subresiduated lattices.

Palabras clave
Spectral duality
Strict implication

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