??? .... "diaconescu's theorem for pre-sheaf topos equipped with day convolution symmetric tensor product" .... ???and generalizations and adaptations of this .... ??? ...

??relationship to ... ???vague feelings about ... "combined doctrine" ... in non-toric case ... ??"flat model" .... ??? with "flat" here trying to have some sort of naive intuitive interpretation .... ???? .....

??? ... monoidal (or perhaps pro-monoidal ...) site category ... for example direct limits of principal N-sets ... "geometric morphism whose lex left adjoint part is symmetric monoidal" .... ... ??? ...

??i think that i vaguely remember that we've already thought about "trying to generalize diaconescu's theorem from the pre-sheaf case to the sheaf case" ... ???....