Stone duality for spectral sheaves and the patch monad

Clemens Berger; Mai Gehrke

doi:10.1016/j.jpaa.2022.107306

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arXiv · 2202.00084

Stone duality for spectral sheaves and the patch monad

Clemens Berger·Mai Gehrke

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Abstract

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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Clemens Berger, Mai Gehrke. 2022-01-31. Stone duality for spectral sheaves and the patch monad. https://doi.org/10.1016/j.jpaa.2022.107306

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