The Grothendieck computability model
Category Theory
2024-04-30 v1
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.
Keywords
Cite
@article{arxiv.2404.17923,
title = {The Grothendieck computability model},
author = {Luis Gambarte and Iosif Petrakis},
journal= {arXiv preprint arXiv:2404.17923},
year = {2024}
}
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12 pages