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arXiv · 2402.08945

Etale spaces of residuated lattices

Saeed Rasouli·Seyed Naser Hosseini·Amin Dehghani
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Abstract

This paper explores the concept of \'{e}tal\'{e} spaces associated with residuated lattices. Notions of bundles and \'{e}tal\'{e}s of residuated lattices over a given topological space are introduced and investigated. For a topological space $\mathscr{B}$, we establish that the category of \'{e}tal\'{e}s of residuated lattices over $\mathscr{B}$ with morphisms of \'{e}tal\'{e}s of residuated lattices is coreflective in the category of bundles of residuated lattices over $\mathscr{B}$ along with morphisms of bundles of residuated lattices. We provide a method for transferring an \'{e}tal\'{e} of residuated lattices over a topological space to another, utilizing a continuous map. Finally, we define a contravariant functor, called the section functor, from the category of \'{e}tal\'{e}s of residuated lattices with inverse morphisms to the category of residuated lattices.

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BibTeXRIS

Saeed Rasouli, Seyed Naser Hosseini, Amin Dehghani. 2024-02-14. Etale spaces of residuated lattices. https://arxiv.org/abs/2402.08945

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