Translating notions and results from category theory to the theory of computability models of Longley and Normann, we introduce the Grothendieck computability model. We define the corresponding first-projection-simulation, and we prove some of its basic properties. With the Grothendieck computability model the category of computability models is shown to be a type-category, in the sense of Pitts, a result that bridges the categorical interpretation of dependent types with the theory of computability models. We introduce the notion of a fibration and opfibration-simulation, and we show that the first-projection-simulation is a split opfibration-simulation.

The Grothendieck Computability Model

Iosif Petrakis
2024-01-01

Abstract

Translating notions and results from category theory to the theory of computability models of Longley and Normann, we introduce the Grothendieck computability model. We define the corresponding first-projection-simulation, and we prove some of its basic properties. With the Grothendieck computability model the category of computability models is shown to be a type-category, in the sense of Pitts, a result that bridges the categorical interpretation of dependent types with the theory of computability models. We introduce the notion of a fibration and opfibration-simulation, and we show that the first-projection-simulation is a split opfibration-simulation.
2024
Computability models, Grothendieck construction, Fibrations
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1144995
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