??so what about ... given functor f:x->y, considering functor _presheaf(x)_ -> _presheaf(y)_ given by ... "taking formal colimit of x-objects to formal colimit of their y-object f-values" ?? ... or something ... seems obvious ... ???...

??relationship to ... ???forgetful (2,1)-functor taking theory of "combined doctrine" to that of uncombined ... ???and so forth ... ???...

??so what about construeing "combined doctrine" here as simply weak pullback of (2,1)-categories of syntactic theories ?? ... or something ... ??...