Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets
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| Format: | Preprint |
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2024
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| _version_ | 1866916474057129984 |
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| author | Rosset, Aloïs Hansen, Helle Hvid Endrullis, Jörg |
| author_facet | Rosset, Aloïs Hansen, Helle Hvid Endrullis, Jörg |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_04535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets Rosset, Aloïs Hansen, Helle Hvid Endrullis, Jörg Logic in Computer Science Category Theory 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. |
| title | Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2407.04535 |