This paper presents a theoretical framework for sheaves and etale spaces in residuated lattices, highlighting their categorical and topological aspects.
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.
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Saeed Rasouli (2025) studied this question.
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