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.
Keywords: MV-algebras, protomodular categories, semiabelian categories, 0-ideals, augmentation ideal, relative ideal, unitalization
2020 MSC: 18C05, 18E13, 06D35, 03B47
Theory and Applications of Categories, Vol. 41, 2024, No. 27, pp 878-893.
Published 2024-07-30.
TAC Home