?? so did we make some sort of really stupid mistake (?? level slip ??) in thinking that alleged absoluteness of colimit weights over _cocomplete cat_ would "make ag correspondences work very nicely" ?? ... ?? because at the moment it's seeming it like it doens't work _that_ nicely .... involving pushing and pulling and running into complications in the non-affine case ... ?? .... existence of coherent sheaf cohomology ... ??? .....

?? need to straighten this all out, obviously ... ??? and ok if things don't work all _that_ "nicely" ... just need to straighten things out enough to understand what's going on with toric quasicoherent tensor product in "co-fan" picture ... ??? ....

?? extra adjoint (?? .... ??? ....) for binary tensor product ... ?? relationship to similar for tensoring with given object ?? ... ??? ... ??? ....

?? how annoying might it be if ... ?? correspondences aren't represented faithfully (...) by functors ... ?? .... ?? ... ?? and are they ?? ...