格罗滕迪克可计算模型

IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Luis Gambarte , Iosif Petrakis
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引用次数: 0

摘要

在将范畴论的概念和结果转化为朗利和诺曼的可计算模型理论的基础上,引入了格罗腾迪克可计算模型。定义了第一次投影模拟,并证明了它的基本性质。在格罗滕迪克可计算模型中,可计算模型的范畴被证明是皮茨意义上的类型-范畴,这一结果将依赖类型的范畴解释与可计算模型理论联系起来。我们还证明了可计算模型的范畴是一个具有2族箭头和相应的sigma对象结构的范畴。最后,我们引入了颤振和颤振仿真的概念,并证明了第一次投影仿真是一个分裂的颤振仿真。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Grothendieck computability model
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 first-projection-simulation and prove 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 also show that the category of computability models is a category with 2-family arrows and a corresponding structure of Sigma-objects. Finally, we introduce the notion of a fibration and opfibration-simulation, and we prove that the first-projection-simulation is a split opfibration-simulation.
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来源期刊
Theoretical Computer Science
Theoretical Computer Science 工程技术-计算机:理论方法
CiteScore
2.60
自引率
18.20%
发文量
471
审稿时长
12.6 months
期刊介绍: Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.
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