Quasitoposes have proven to be an interesting framework for many graph rewriting formalisms. Since presheaves categories are toposes and fuzzy sets are quasitoposes, we prove that the combination of both, fuzzy presheaves, are also quasitoposes. This question was recently conjectured more specifically for fuzzy graphs and is now therefore proven. This entails that many fuzzy presheaves of interest can be used for graph rewriting.

翻译：拟拓扑已被证明是许多图重写形式化方法的有效框架。鉴于预层范畴是拓扑结构，而模糊集是拟拓扑结构，我们证明二者的结合——模糊预层——同样构成拟拓扑。最近有猜想更具体地针对模糊图提出此问题，现已被证实。这意味着许多有意义的模糊预层可应用于图重写。