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Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2023

Stone duality for spectral sheaves and the patch monad

Mai Gehrke

Résumé

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.

Dates et versions

hal-03613205 , version 1 (18-03-2022)

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Clemens Berger, Mai Gehrke. Stone duality for spectral sheaves and the patch monad. Journal of Pure and Applied Algebra, 2023, 227 (6), pp.107306. ⟨10.1016/j.jpaa.2022.107306⟩. ⟨hal-03613205⟩
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