Quasitoposes encompass a wide range of structures, including various categories of graphs. They have proven to be a natural setting for reasoning about the metatheory of algebraic graph rewriting. In this paper we propose and motivate the notion of fuzzy presheaves, which generalises fuzzy sets and fuzzy graphs. We prove that fuzzy presheaves are rm-adhesive quasitoposes, proving our recent conjecture for fuzzy graphs. Furthermore, we show that simple fuzzy graphs categories are quasitoposes.

翻译：拟拓扑涵盖广泛的结构，包括多种图范畴。它们已被证明是代数图重写元理论推理的自然框架。本文提出并论证了模糊预层的概念，该概念推广了模糊集与模糊图。我们证明模糊预层是rm-可粘合拟拓扑，从而证实了我们近期关于模糊图的猜想。此外，我们证明了简单模糊图范畴是拟拓扑。