A 2-categorical proof of Frobenius for fibrations defined from a generic point

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2024-04-15 DOI:10.1017/s0960129524000094

Sina Hazratpour, Emily Riehl

引用次数: 0

Abstract

Consider a locally cartesian closed category with an object

$\mathbb{I}$

and a class of trivial fibrations, which admit sections and are stable under pushforward and retract as arrows. Define the fibrations to be those maps whose Leibniz exponential with the generic point of

$\mathbb{I}$

defines a trivial fibration. Then the fibrations are also closed under pushforward.

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从一般点定义的纤维的弗罗贝尼斯二分类证明

考虑一个具有对象 $\mathbb{I}$ 和一类琐细纤度的局部笛卡尔封闭范畴，这些琐细纤度允许分段，并且在作为箭头的前推和后撤下是稳定的。定义纤度为那些其与 $\mathbb{I}$ 的泛点的莱布尼兹指数定义了琐碎纤度的映射。那么这些纤度在推挽作用下也是封闭的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.