Twist structures and Nelson conuclei
Rings and Algebras
2021-07-30 v1 Logic
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.
Cite
@article{arxiv.2107.14198,
title = {Twist structures and Nelson conuclei},
author = {Manuela Busaniche and Nikolaos Galatos and Miguel Andrés Marcos},
journal= {arXiv preprint arXiv:2107.14198},
year = {2021}
}