Emergent Mind

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

(2407.04535)

Published Jul 5, 2024 in cs.LO and math.CT

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.

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