Stone duality for spectral sheaves and the patch monad (Q2689181)

This paper deals with a sheaf-theoretical extension of Stone duality, which is a dual equivalence between global sheaves on spectral spaces and right distributive bands (Theorem 3.6). The benefit of a duality over general spectral spaces is the interaction with the so-called patch topology [\textit{M. Hochster}, Trans. Am. Math. Soc. 142, 43--60 (1969; Zbl 0184.29401); \textit{A. Grothendieck}, Publ. Math., Inst. Hautes Étud. Sci. 17, 137--223 (1963; Zbl 0122.16102)], giving rise to a patch monad on sheaves over a fixed spectral space. Under the duality just mentioned the algebras of the patch monad are shown to correspond to distributive skew lattices.