?? extra "toric convolution" tensor product ... modules of commutative bialgebra .... ??? "bialgebra dual" here ??? ... ??? what happens if you try to "switch roles of the two tensor products ("commutative" and "comultiplication" ...) without dualizing thre bialgebra" ???

??? superman-flavor equivalence theorem between "bialgebra" (?? ...) and "nice monoidal category" .... ???.... what happens to such in "globalized" context ?? .... ???? "generalized day convolution" ????? .....

??set-based vs vsp-based such (? ...) theorem .... ?? ... day convolution ... ?? "tannaka-krein" ??? ... .... ??? "set-based tannaka-krein / tannakian program / philosophy" ... ?? well, that _is_ sort of what this (...) toric stuff is about .... ??? ....

?? some sort of unification of "grothendieck topology" and "specification of filtered colimits to be preserved" ??? .... ???? ....

?? generalized day convolution and ... ??? superman-flavor equivalence theorem between tensor product operation on nice category and "virtual" such on corresponding "site" ??? ..... ??? .... ??? ...