On the categorical behaviour of V-groups

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Clementino, Maria Manuel¹  Montoli, Andrea² 

[1] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra, Portugal

[2] Univ Milan, Dipartimento Matemat Federigo Enriques, Via Saldini 50, I-20133 Milan, Italy

关键词: V-category;    V-group;    Protomodular object;    Metric and ultrametric group;   

DOI  :  10.1016/j.jpaa.2020.106550

来源: Elsevier

【 摘 要 】

We consider compatible group structures on a V-category, where V is a quantale, and we study the topological and algebraic properties of such groups. Examples of such structures are preordered groups, metric and ultrametric groups, probabilistic (ultra)metric groups. In particular, we show that, when V is a frame, symmetric V-groups satisfy very strong categorical-algebraic properties, typical of the category of groups. In particular, symmetric V-groups form a protomodular category. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free