?? x toric variety ...

?? y open sub-[toric variety] ...

(secretly x = spec(n), y = spec(z) ... ?? to try to get things straight ... ??? ...)

left adjoint "localization" from tqcs(x) to tqcs(y) .... ?? ...

?? then consider .... ??? taking "structure sheaf" of y ..... ???? and then applying the _right_ adjoint to it ?? .... ?? in affine case simply the underlying action ??? .... ?? ....

?? so then how do these objects of tqcs(x) (coming from the basic y's ... ??? ...) relate to the objects of the co-fan category ??????? ..... ????? hmmm, hom-sets that we (maybe ... ?? ...) worked out at some point ????? ....

?? if the categories here are equivalent then we really need to understand how / why ... ??? ....