Algebras with implication and fusion: a different point of view

This work uses well-known results on tensor products of lattices and semilattices developed by Fraser and Grätzer et al., and the duality for bounded distributive lattices introduced by Cignoli et al., in order to develop dual categorical equivalences involving bounded distributive lattices with fusion and implication, respectively. We show that these equivalences are essentially those developed by Cabrer and Celani as part of the PhD thesis of the former.Fil: Castiglioni, José Luis. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: San Martín, Hernán Javier. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentin