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

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Serafina Lapenta, Giuseppe Metere, and Luca Spada

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.

http://www.tac.mta.ca/tac/volumes/41/27/41-27.pdf

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