??sheaf and/or pre-sheaf of commutative monoids ...

??something about getting from a commutative monoid its filteredly cocompletion ... ??or something ... ??something about in contravariant way, or something ????....

????.....

pre-sheaf of actions over a pre-sheaf of ocmmutative monoids ... ??_is_ this just a pre-sheaf over some category somewhat straightforwardly obtained from the pre-sheaf of ocmmutative monoids ???? ..... and so forth .... ????....

??what about something about "toric quasicoherence" here ???? .... and so forth ... ???....

???lots of confusion ??? ....

??what about idea that "the crucial aspect of quasicoherence is in the affine case" (or something...) in this (...) toric case ??? .... ??and so forth ... ...hmmm....