??so consider the "toric ag theory" of... ???

??well, consider the graded actions of the free Z-graded commutative monoid on n+1 generators in grade 1 ...

??which we can think of as forming a pre-sheaf topos?? ... objects of site category = integers .... morphisms = ... ???..

??but then consider the sheaves for a certain topology here ??...


??so what about something about... ??the per-sheaf topos here as a slice topos, and some conceptual interpretation of that ... ???and so forth ... ???

???something about ... ??torsor of group completion of commutative monoid ... ???something about with frame for certain associated torsor ... ???or something ???.... and so forth ... ????

??maybe reminding me of something about toric varieties here, in fact ??? ....