Geodesic
Categorical-Algebraic Properties of Lattice-ordered Groups
Theory and applications of categories, Tome 39 (2023), pp. 916-948

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

We study the categorical-algebraic properties of the semi-abelian variety lGrp of lattice-ordered groups. In particular, we show that this category is fiber-wise algebraically cartesian closed, arithmetical, and strongly protomodular. Moreover, we observe that lGrp is not action accessible, despite the good behaviour of centralizers of internal equivalence relations. Finally, we restrict our attention to the subvariety lAb of lattice-ordered abelian groups, showing that it is algebraically coherent; this provides an example of an algebraically coherent category which is not action accessible.

Publié le :
Classification : 06F15, 18E13
Keywords: lattice-ordered group, semi-abelian category, algebraically coherent category 
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     author = {Andrea Cappelletti},
     title = {Categorical-Algebraic {Properties} of {Lattice-ordered} {Groups}},
     journal = {Theory and applications of categories},
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     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a30/}
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Andrea Cappelletti. Categorical-Algebraic Properties of Lattice-ordered Groups. Theory and applications of categories, Tome 39 (2023), pp. 916-948. http://geodesic.mathdoc.fr/item/TAC_2023_39_a30/