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.

翻译：单纯形集可推广多种图范畴。本文完整刻画了（半）单纯形集、双色图及模糊集上的Lawvere-Tierney拓扑结构。应用所得结果，我们证明了“部分单纯”单纯形集与“部分单纯”图构成拟拓扑斯。