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

Aloïs Rosset; Helle Hvid Hansen; Jörg Endrullis

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

Aloïs Rosset
, Helle Hvid Hansen
, Jörg Endrullis

Research output: Working paper / Preprint › Preprint › Academic

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Abstract

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.

Original language	English
Publication status	Published - 5 Jul 2024

Keywords

cs.LO
math.CT

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2407.04535v1

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1 Conference contribution

Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets
Rosset, A., Hansen, H. H. & Endrullis, J., 2026, Logic, Language, and Computation - 14th International Tbilisi Symposium, TbiLLC 2023, Revised Selected Papers. Hogeweg, L., Jalali, R., Sedlár, I. & Schwarz, L. (eds.). Springer Nature Switzerland AG, p. 258-284 27 p. (Lecture Notes in Computer Science; vol. 15661 LNCS)(TbiLLC: International Tbilisi Symposium on Logic, Language, and Computation; vol. 2023).
Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

Cite this

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AB - 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.

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

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Keywords

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Research output

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

Cite this