Stone duality for spectral sheaves and the patch monad
We establish a duality between global sheaves on spectral spaces and right distributive bands. This is a sheaf-theoretical extension of classical Stone duality between spectral spaces and bounded distributive lattices. The topology of a spectral space admits a refinement, the so-called patch topolog...
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Veröffentlicht in: | Journal of pure and applied algebra 2023-06, Vol.227 (6), p.107306, Article 107306 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We establish a duality between global sheaves on spectral spaces and right distributive bands. This is a sheaf-theoretical extension of classical Stone duality between spectral spaces and bounded distributive lattices.
The topology of a spectral space admits a refinement, the so-called patch topology, giving rise to a patch monad on sheaves over a fixed spectral space. Under the duality just mentioned the algebras of this patch monad are shown to correspond to distributive skew lattices. |
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ISSN: | 0022-4049 1873-1376 |
DOI: | 10.1016/j.jpaa.2022.107306 |