Computability models over categories
arXiv:2105.06933
Abstract
Generalising slightly the notions of a strict computability model and of a simulation between them, which were elaborated by Longley and Normann, we define canonical computability models over categories and appropriate Set-valued functors on them. We study the canonical total computability model over a category, and the partial one over a category with pullbacks. Our notions and results are generalised to categories with a base of computability, connecting Rosolini's theory of dominions with the theory of computability models.
8 pages