Geodesic
Relative ideals in homological categories with an application to MV-algebras
Theory and applications of categories, Tome 41 (2024), pp. 878-893

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
Classification : 18C05, 18E13, 06D35, 03B47
Keywords: MV-algebras, protomodular categories, semiabelian categories, 0-ideals, augmentation ideal, relative ideal, unitalization 
@article{TAC_2024_41_a26,
     author = {Serafina Lapenta and Giuseppe Metere and Luca Spada},
     title = {Relative ideals in homological categories with an application to {MV-algebras}},
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     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a26/}
}
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Serafina Lapenta; Giuseppe Metere; Luca Spada. Relative ideals in homological categories with an application to MV-algebras. Theory and applications of categories, Tome 41 (2024), pp. 878-893. http://geodesic.mathdoc.fr/item/TAC_2024_41_a26/