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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.08945 |
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| _version_ | 1866910330927448064 |
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| author | Rasouli, Saeed Hosseini, Seyed Naser Dehghani, Amin |
| author_facet | Rasouli, Saeed Hosseini, Seyed Naser Dehghani, Amin |
| contents | This paper explores the concept of étalé spaces associated with residuated lattices. Notions of bundles and étalés of residuated lattices over a given topological space are introduced and investigated. For a topological space $\mathscr{B}$, we establish that the category of étalés of residuated lattices over $\mathscr{B}$ with morphisms of étalés 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 étalé 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 étalés of residuated lattices with inverse morphisms to the category of residuated lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08945 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Etale spaces of residuated lattices Rasouli, Saeed Hosseini, Seyed Naser Dehghani, Amin Rings and Algebras Algebraic Geometry Category Theory This paper explores the concept of étalé spaces associated with residuated lattices. Notions of bundles and étalés of residuated lattices over a given topological space are introduced and investigated. For a topological space $\mathscr{B}$, we establish that the category of étalés of residuated lattices over $\mathscr{B}$ with morphisms of étalés 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 étalé 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 étalés of residuated lattices with inverse morphisms to the category of residuated lattices. |
| title | Etale spaces of residuated lattices |
| topic | Rings and Algebras Algebraic Geometry Category Theory |
| url | https://arxiv.org/abs/2402.08945 |