Right-preordered groups from a categorical perspective

2024/06/14 by Maria Manuel Clementino, Clementino, Maria Manuel, Andrea Montoli +1
Computer Science · Mathematics · #06F05 #06F15 #18E08 #18E13 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2406.10071

openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, and studying some exactness properties. We show that, from an algebraic point of view, the category of right-preordered groups shares several properties with the one of monoids. Moreover, we describe split extensions of right-preordered groups, showing in particular that semidirect products of ordered groups have always a natural right-preorder.

Related

• The stable category of preordered groups
• On split extensions of preordered groups
• Central extensions of preordered groups
• Some algebraic and topological properties of subspaces of (pre)orders
• Schreier split extensions of preordered monoids