Stratified L-convex groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909443467247616 |
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| author | Li, Lingqiang Jin, Qiu |
| author_facet | Li, Lingqiang Jin, Qiu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stratified L-convex groups Li, Lingqiang Jin, Qiu General Topology 52A01, 54A40, 54A20 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. |
| title | Stratified L-convex groups |
| topic | General Topology 52A01, 54A40, 54A20 |
| url | https://arxiv.org/abs/2412.19014 |