Stratified L-convex groups
Abstract
This paper investigates a novel structure of stratified L-convex groups, defined as groups possessing stratified L-convex structures, in which the group operations are L-convexity-preserving mappings. It is verified that stratified L-convex groups serve as objects, while L-convexity-preserving group homomorphisms serve as morphisms, together forming a concrete category, denoted as SLCG. As a specific instance of SLCG (i.e., when L=2), the category of convex groups, denoted as CG, is also defined. We show that CG can be embedded within SLCG as a reflective subcategory. In addition, we demonstrate that SLCG possesses well-defined characterizations, localization properties, and initial and final structures, establishing it as a topological category over groups.
Cite
@article{arxiv.2412.19014,
title = {Stratified L-convex groups},
author = {Lingqiang Li and Qiu Jin},
journal= {arXiv preprint arXiv:2412.19014},
year = {2024}
}