Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets
Aloïs Rosset, Helle Hvid Hansen, Jörg Endrullis · arXiv (Cornell University) · 2024
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.