Stratified L-convex groups

2024/12/26 by Li, Lingqiang, Jin, Qiu
#52A01 #54A20 #54A40 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2412.19014

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.

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