标题： 残差格层 显示英文标题

标题： Sheaf of Residuated Lattices

摘要： 本文通过为剩余格构建层和埃塔尔空间的理论，探讨了代数、拓扑学和逻辑之间的界面，这些代数结构是子结构性和模糊逻辑的核心。 我们构造了逐点剩余的埃塔尔空间，并证明它们是集合埃塔尔空间范畴的一个子范畴。 提出了层条件的范畴和拓扑特征，特别强调滤子、同余关系以及在素谱上诱导的拓扑。 显示英文摘要

摘要： This paper explores the interface between algebra, topology, and logic by developing the theory of sheaves and etale spaces for residuated lattices, algebraic structures central to substructural and fuzzy logics. We construct stalkwise-residuated etale spaces and demonstrate that they form a subcategory of the category of etale spaces of sets. A categorical and topological characterization of the sheaf condition is presented, with particular emphasis on filters, congruences, and the topologies induced on prime spectra.