2023/10/13 by Andrea Cappelletti, Cappelletti, Andrea
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2310.09264
openalex publication_date 2023/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the categorical-algebraic properties of the semi-abelian variety ℓ \mathbbGrp 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 ℓ \mathbbGrp is not action accessible, despite the good behaviour of centralizers of internal equivalence relations. Finally, we restrict our attention to the subvariety ℓ \mathbbAb 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.