Exponentiation in V-categories

• Author(s): Clementino, Maria Manuel ; Hofmann, Dirk
• Date: 2006
• Persistent ID: http://hdl.handle.net/10316/4614
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Exponentiable object; Exponentiable morphism; V-category; Premetric space; Almost convex metric space; Totally convex metric space
• Document Type: Article
• Language: English

Description

For a Heyting algebra V which, as a category, is monoidal closed, we obtain characterizations of exponentiable objects and morphisms in the category of V-categories and apply them to some well-known examples. In the case these characterizations of exponentiable morphisms and objects in the categories (P)Met of (pre)metric spaces and non-expansive maps show in particular that exponentiable metric spaces are exactly the almost convex metric spaces, while exponentiable complete metric spaces are the complete totally convex ones. http://www.sciencedirect.com/science/article/B6V1K-4GYH7FT-1/1/440d88b88811e29112fc189c682537b3