Talk:Completely distributive lattice
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Left adjoint
For a set X, the left adjoint of the union map from the set of lower sets of the power set of X to the power set of X sends the empty set to the empty set and each nonempty subset Y to the lower set consisting of the empty set and singletons containing elements of Y. That makes the power set a completely distributive lattice. GeoffreyT2000 (talk) 15:57, 8 June 2015 (UTC)