The Grothendieck computability model

Abstract

Translating notions and results from category theory to the theory of computability models of Longley and Normann, we introduce the Grothendieck computability model and the first-projection-simulation. We prove some basic properties of the Grothendieck computability model, and we show that the category of computability models is a type-category, in the sense of Pitts. We introduce the notion of a fibration and opfibration-simulation, and we show that the first-projection-simulation is a split opfibration-simulation.