2022/08/26 by Serafina Lapenta, Lapenta, Serafina, Giuseppe Metere +3 · 3 citations
Computer Science · #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2208.12597
openalex publication_date 2022/08/26 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28
Let A be a homological category and U\colon B→ A be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to U, and we show that, under suitable conditions, any object of A can be seen as a relative ideal of some object in B. We then develop a case study. We first prove that the category of hoops is semi-abelian and that the category of MV-algebras is protomodular, then we apply our results to the forgetful functor from the category of MV-algebras to the category of Wajsberg hoops.