Homotopical characterization of strongly contextual simplicial distributions on cone spaces

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-05-18 DOI:10.1016/j.topol.2024.108956

Aziz Kharoof, Cihan Okay

引用次数: 0

Abstract

This paper offers a novel homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined on the cone of a 1-dimensional space. In the sheaf-theoretic framework, such distributions correspond to non-signaling distributions on measurement scenarios where each context contains 2 measurements with binary outcomes. To establish our results, we employ a homotopical approach that includes collapsing measurement spaces and introduce categories associated with simplicial distributions that can detect strong contextuality.

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圆锥空间上强上下文简约分布的同向表征

本文对具有二进制结果的强上下文简约分布，特别是那些定义在一维空间锥体上的分布，提出了一种新的同向表征。在 Sheaf 理论框架中，这种分布对应于测量场景中的非信号分布，其中每个上下文包含 2 个具有二进制结果的测量。为了建立我们的结果，我们采用了一种同托邦方法，其中包括折叠测量空间，并引入了与简约分布相关的类别，这些类别可以检测强上下文性。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.

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