??so what _about_ relationship / interaction between various (??partial ...???) "booleanization" processes ... namely, "double-negation topology" and ... ???adjoining of complements ... ??also "keeping only the complemented things", i suppose ... ??what _about_ weirdness of "double-negation" process... ??as not an adjoint functor in any very obvious way ... ??or something ...

something about examples that we've been considering where first we throw in some complements, then take double-negation topology ... ??... ??roughly, "because if you didn't throw in those complements then the double-negation process would be too destructive... too many "collapse morphisms" ..." ....???...