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arXiv · 2407.04535

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

Aloïs Rosset·Helle Hvid Hansen·Jörg Endrullis
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Abstract

Simplicial sets generalise many categories of graphs. In this paper, we give a complete characterisation 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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Aloïs Rosset, Helle Hvid Hansen, Jörg Endrullis. 2024-07-05. Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets. https://arxiv.org/abs/2407.04535

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