A Categorial Equivalence for semi-Nelson algebras
Juan Manuel Cornejo, Andr\'es Gallardo, and Ignacio Viglizzo
TL;DR
This paper establishes a categorical equivalence between semi-Nelson algebras and pairs of semi-Heyting algebras with specific filters, extending to dually hemimorphic cases without filters.
Contribution
It introduces a new categorical framework linking semi-Nelson algebras to semi-Heyting algebra pairs, clarifying their structural relationship.
Findings
Category equivalent to semi-Nelson algebras via semi-Heyting pairs
Filters contain all dense elements and satisfy a technical condition
Equivalence extends to dually hemimorphic semi-Nelson algebras without filters
Abstract
We present a category equivalent to that of semi-Nelson algebras. The objects in this category are pairs consisting of a semi-Heyting algebra and one of its filters. The filters must contain all the dense elements of the semi-Heyting algebra and satisfy an additional technical condition. We also show that in the case of dually hemimorphic semi-Nelson algebras, the filters are not necessary and the category is equivalent to that of dually hemimorphic semi-Heyting algebras.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.