??so given a dg algebroid s and a dg s-module w, we want a dg s-opmodule w* st weakly homming w into another dg s-module x is equivalent to weakly tensoring x with w* ... ??or something...

??and we want to try to understand a couple of alleged motivating examples...

in particular... take s to be the "walking morphism" dg algebroid, and take w to be the "walking kernel element" dg s-module ... ??or something?? ??speaking so far in terms of _"strict"_ universal properties... i think... and we also think that the walking kernel element dg s-module is, from the weak viewpoint, actually the walking homotopy kernel element .... ??or something... but anyway, we're hoping (we think...) that w* here is ... ???a certain shift of the dg s-opmodule that in some (hopefully somewhat obvious, though i don't quite see it yet) sense represents "homotopy cokernel" ... ??or something???