Algebraic exponentiation and action representability for V-groups
Abstract
We show that the category of V-groups, where V is a cartesian quantale, so in particular the category of preordered groups, is locally algebraically cartesian closed with respect to the class of points underlying the product V-category structure. We obtain this by observing that such points correspond to (V-Cat)-enriched functors from a V-group, seen as a one-object V-category, to the category V-Grp of V-groups. Moreover, we show that the actions corresponding to points underlying the product V-category structure are representable.
Fields of Study & Subjects
Advanced Algebra and Logic
Homotopy and Cohomology in Algebraic Topology
Logic
programming
and type systems
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 February 2026
- Language
- EN
- Document type
- Preprint