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arXiv · 2107.14198

Twist structures and Nelson conuclei

Manuela Busaniche·Nikolaos Galatos·Miguel Andrés Marcos
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Abstract

Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to the non-commutative setting. We study their structure, establish a representation theorem for them in terms of twist structures and conuclei that results in a categorical adjunction, and explore situations where the representation is actually an isomorphism. In the latter case, the adjunction is elevated to a categorical equivalence. By applying this representation to the original motivating special cases we bring to the surface their underlying similarities.

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BibTeXRIS

Manuela Busaniche, Nikolaos Galatos, Miguel Andrés Marcos. 2021-06-18. Twist structures and Nelson conuclei. https://arxiv.org/abs/2107.14198

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