I've come across a set of slides by Guram Bezhanishvili where he claims the category of compact hausdorff spaces is related by duality to de Vries algebras. What are they?
See his article "Stone duality and Gleason covers through de Vries duality" in Topology and its Applications 157:1064--1080, 2010, Definition 3.2.
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3 years ago