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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.
@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}},
journal = {Theory and applications of categories},
pages = {878--893},
publisher = {mathdoc},
volume = {41},
year = {2024},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a26/}
}
TY - JOUR AU - Serafina Lapenta AU - Giuseppe Metere AU - Luca Spada TI - Relative ideals in homological categories with an application to MV-algebras JO - Theory and applications of categories PY - 2024 SP - 878 EP - 893 VL - 41 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2024_41_a26/ LA - en ID - TAC_2024_41_a26 ER -
%0 Journal Article %A Serafina Lapenta %A Giuseppe Metere %A Luca Spada %T Relative ideals in homological categories with an application to MV-algebras %J Theory and applications of categories %D 2024 %P 878-893 %V 41 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_2024_41_a26/ %G en %F TAC_2024_41_a26
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/