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.

On the categorical behaviour of V-groups / M.M. Clementino, A. Montoli. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 225:4(2021), pp. 106550.1-106550.24. [10.1016/j.jpaa.2020.106550]

On the categorical behaviour of V-groups

A. Montoli
2021

Abstract

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.
Metric and ultrametric group; Protomodular object; V-category; V-group
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/868048
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