??so let x be a boolean algebra, and consider the category where an object is "a set with x-valued existence and equality predicates" ... ???or something ???... ??maybe some sort of localization here ??? .... ????....

??so given such a set, consider ... ???assigning to each element x1 of x the set obtained by "promoting x1 to true" ... ???or something ... ???....

??relationship to sheaf over corresponding stone space ?? ... ??... and so forth ... ???something about "boolean-valued model", or _something_ ??? ....

??so what about going the other way?? ... starting with sheaf over stone space (or something...) and obtaining "set with x-valued existence and equality predicates" ... ???in maybe obvious way??? ...???something about ... vague feeling about ... ???something about ... ??"injective" or something??? ... something about "injective resolution" ??? ... ?????or something???? .... ???what about _heyting_ algebra case ??? ... or something ... ??and so forth ... ???...