?? graded action x of g-graded commutative monoid m ... ?? m-equivariant map from x to g ??? ...

?? case x invertible ... ??? ..... cartesian power of x ... ??? ....

m -> g .... ???? .... displacement .... ???? .....

m^n -> g .... ??? ....

?? re-expressing toric convolution of given quasicoherent sheaves as particular quasicoherent sheaf .... ??? .... universal property wrt combined doctrine as stronger .... ??? .......

??? "flat" ..... ????? .....