Relative ideals in homological categories with an application to MV-algebras (Q6589558)

The authors' abstract says: ``Let \(\mathsf{A}\) be a homological category and \(U:\mathsf{B}\to\mathsf{A}\) be a faithful conservative right adjoint. We introduce the notion of \textit{relative ideal} with respect to \(U\) and show that, under suitable conditions, any object of \(\mathsf{A}\) can be seen as a relative ideal of some object in \(\mathsf{B}\). We then develop a \textit{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.''\N\NWhat makes this paper particularly interesting and useful is that extending a result of \textit{P. Johnstone} [Fields Inst. Commun. 43, 317--318 (2004; Zbl 1079.08006)] from Heyting semilattices to hoops it establishes a stronger connection between \textit{semi-abelian categorical algebra} and the study of universal algebras related to non-classical logics.