?? categorified bialgebra associated to toric variety .... ??? ... taking it (the idea ... ?? ...) seriously ...

(?? some confusion here between .... tensor product of comm rings, vs tensor product associated to a comm ring .... ???? ....)

?? module of comm ring (?? also comm monoid case ??? ... ???? ...) giving bi-module in hopefully obvious way .... ???generalization of this to other stable tensor cats ??? ..... ??? is this a significant extra thing to ask for, or more automatic, or what ??? .... ??? .... ?? traditional quasicoherent sheaf case ... ??? ....

?? "tannaka-krein" ideas here ... ??? .... ?? lots of level slipping here ??? .....

?? relationship between ["mayhem vs doctrine" ... ??? ...] and ["operations on models" and / or "multi-model stuff ..." ... ??? .... ??? ...] ?? ..... ??? unclear ?? .... ??? ... to me at the moment, at least .... ??? ....

?? relationship between [relationship between toric quasicoherent sheaf (?? ...) and "toric convolution cocomm comonoid" ... ?? ...] and [relationship between toric line bundles (?? ...) and "graded commutative monoid" ... ?? ...] ?? ... ??? "grading" ... "convolution" .... ???? ..... ??? fourier duality ... grading / acting .... ?? ... ???? ....

?? some days you get the woozle and some days the woozle gets you .... ??? ...