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

  • 会议论文

  • 发表日期：

    2026年

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  • Aloïs Rosset,
  • Helle Hvid Hansen,
  • Jörg Endrullis

摘要

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 bicoloured graphs, and on fuzzy sets. We apply our results to establish that ‘partially simple’ simplicial sets and ‘partially simple’ graphs form quasitoposes.