?? quasicoherent sheaf over toric variety that's (at least locally ... ?? ...) toric convolution comonoidal, and also ordinary pointwise tensor monoidal, or comonidal, or whatever ... ???? ....

case where convolution comonoidal structure is/n't "discrete" .... ???? ....

??? invertibility wrt toric convolution tensor product .... ????

?? relationship to generalized ("translational" ... ?? ...) morphism of toric varieties .... ??? ....

?? seeing via "ordinary AG interpretation of underlying ordinary quasicoherent sheaf of toric quasicoherent sheaf" how concept of "toricness" of quasicoherent sheaf depends on "basepoint(s?)" of toric variety .... ??? .... ?? but then idea of "allowing translates of toric quasicoherent sheaves" (?? ...), and how that might relate to other (more "TAG-intrinsic" ... ???...) ideas about what happens to accidental topos when TAG is "mad emore translation-independent" by using generalized morphisms of toric varieties ...

??? toric convolution of torically equivariant stuff .... ??? decategorifies to "convolution of constant functions" ???? ..... which sounds weirdly degenerate, but .... ??? maybe more interesting categorified ?? .... ??? ....

???? _are_ (?? some ?? ...) line bundles on toric varieties maybe simultaneously toric-convolution-comonoidal and toric-equivariant ???? ..... ??????? ..... ????? ....... ?? hmmm .... ??? magic of invertibility ... ???? ....