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.

翻译：单纯集可推广诸多图范畴。本文对（半）单纯集、双色图及模糊集上的Lawvere-Tierney拓扑给出了完整刻画。我们应用所得结果证明了“部分单纯”单纯集与“部分单纯”图构成拟拓扑斯。