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arXiv · 2404.17923

The Grothendieck computability model

Luis Gambarte·Iosif Petrakis
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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.

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Luis Gambarte, Iosif Petrakis. 2024-04-27. The Grothendieck computability model. https://arxiv.org/abs/2404.17923

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