tensor powers ... of bialg .... prop .... as toric convolution powers of unit quasicoherent sheaf over toric variety ... ... .... ???? props involved in non-affine case ???? ...... ..... fan .... ???? ..... ???? ... ??? "re-using fan" ??? ..... ???? see "flat toric monic" below ... ??? .....

?? also projective case and graded bialgebra ... ??? ....

?? hmmm ... ?? this idea above of tensor powers of bistable bialgebra as toric convolution powers of unit ordinary quasicoherent sheaf over toric variety (?? and then maybe doing some stuff with this that i didn't spell out too clearly yet ...) ... ?? combining this with relationship between toric convolution of ordinry quasicoherent sheaves and cartesian product of toric quasicoherent sheaves ... ??? .... hmmmm ..... ??? relationship to ideas about .... ??? ... revisionist idea of defining "group" as "not neccessarily cocommutative hopf object" and recovering original (?? ...) case as special case where symmetric monoidal environment of model has property (...) of being cartesian ... ?? ..... ???? .... ??? .... topos ... ??? .....

what we're supposed to be working on ... ?? tensor product as "generalized day convolution" ... various sort sof geometric interpretations ... trying to straighten out .... for paper .... ???? ....

flat toric monic ... ?? ... ??? does monic requirement for flatness in toric case make good conceptual sense ?? .... ????? .....