Let A be a homological category and U: B → A be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to U and 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.
RELATIVE IDEALS IN HOMOLOGICAL CATEGORIES WITH AN APPLICATION TO MV-ALGEBRAS
Lapenta S.;Metere G.;Spada L.
2024
Abstract
Let A be a homological category and U: B → A be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to U and 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.File in questo prodotto:
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