?? doctrine of bialgebras .... ???? level slips .... ???? ..... ?????? .......

?? "commutative ring equipped with extra toric convolution operation on its modules" ... ??? ??? toric convolution powers of the cayley-yoneda module ... ???? .... ????? .....

?? "graded commutative ring equipped with extra toric convolution operation on its graded modules" .... ???? .... graded bialgebra ..... ???? ..... ???? .....

?? trying to work out whole bit about ... "toric geometric morphism interpretation of tensor product of toric quasicoherent sheaves" .... ????? .....