2021/05/14 by Iosif Petrakis, Petrakis, Iosif
Computer Science · Mathematics · #Category Theory (math.CT) #Computability, Logic, AI Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2105.06933
openalex publication_date 2021/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.