H and Q commute on well-filtered dcpo L iff L satisfies (KC) and Scott topology coincides with upper Vietoris on Q(L); the composed monad's Eilenberg-Moore category is a subcategory of Frm.
Vickers, The double powerlocale and exponentiation: a case study in geometric logic, Theory and Applications of Categories , 12 (2004): 372-422
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Commutation of Smyth and Hoare Power Constructions in Well-filtered Dcpos
H and Q commute on well-filtered dcpo L iff L satisfies (KC) and Scott topology coincides with upper Vietoris on Q(L); the composed monad's Eilenberg-Moore category is a subcategory of Frm.