Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets
<|reference_start|>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.<|reference_end|>
@article{rosset2024characterisation,
    title={Characterisation of Lawvere-Tierney Topologies on Simplicial Sets,
  Bicolored Graphs, and Fuzzy Sets},
    author={Alo"is Rosset, Helle Hvid Hansen, J"org Endrullis},
    journal={arXiv preprint arXiv:2407.04535},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.04535},
    primaryClass={cs.LO math.CT}
}