?? to what extent can module category of bialgebra be thought of as "categorification" of the bialgebra ??? ....

?? some very basic presumably old questions here that i don't have much idea how to answer ... ??? ...

?? whatever it is that bialgebra structure on commutative algebra lets you do to modules, to what extent does toric structure on variety let you do it to quasicoherent sheaves ?? ... ??? maybe a lot ??? ... ?? feeling that there's something missing as ... ?? slippery phantom ?? ... ??? ?? co-binary operation adjoint to toric convolution ??? ... ??? ....

?? co-modules as what's missing ?? ... ??? .... ??? .... ??? ....

?? functorial operations preserved by bimodule homs ... and/or "toric maps" ... ??? ....

bimonoid vs bimonoid .... ???? ...hopf ... frobenius ... "algebraic" manifestation of "haar measure" .... compactness ... serre duality ... verdier duality .... ??...