Weakly monadic Boolean extension functors
We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.
We investigate σ-entangled linear orders and narrowness of Boolean algebras. We show existence of σ-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the behavior of these notions in ultraproducts.