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

62 Downloads (Pure)

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

Access to Document

2407.04535v1

Persistent URL (handle)

Persistent link

Cite this

@techreport{ad8ebec986d7470fafba7c769774530b,

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

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.",

keywords = "cs.LO, math.CT",

author = "Alo{\"i}s Rosset and Hansen, {Helle Hvid} and J{\"o}rg Endrullis",

year = "2024",

month = jul,

day = "5",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets

AU - Rosset, Aloïs

AU - Hansen, Helle Hvid

AU - Endrullis, Jörg

PY - 2024/7/5

Y1 - 2024/7/5

N2 - 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.

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.

KW - cs.LO

KW - math.CT

M3 - Preprint

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

ER -

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

Abstract

Keywords

Access to Document

Persistent URL (handle)

Fingerprint

Cite this