简约集、双色图和模糊集上的 Lawvere-Tierney 拓扑特征

arXiv - MATH - Category Theory Pub Date : 2024-07-05 DOI:arxiv-2407.04535

Aloïs Rosset, Helle Hvid Hansen, Jörg Endrullis

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引用次数: 0

摘要

简单集概括了许多图形类别。在本文中，我们给出了关于（半）简单集、双色图和模糊集的 Lawvere-Tierney 拓扑的完整描述。我们应用我们的结果确定了 "部分简单 "的单纯集和 "部分简单 "的图构成准拓扑。

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Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets

Simplicial sets generalize many categories of graphs. In this paper, we give a complete characterization of the Lawvere-Tierney topologies on (semi-)simplicial sets, on bicolored graphs, and on fuzzy sets. We apply our results to establish that 'partially simple' simplicial sets and 'partially simple' graphs form quasitoposes.

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arXiv - MATH - Category Theory

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