?? so let's try guessing ag correspondence for toric convolution on projective line, for example ... ??? ....

?? n-ary toric convolution .... ??? ..... [projective line]^[n+1] ... ??? ... ?? n-ary addition / multiplication ... ??? partially-defined .... ???? .... codimension 1 _quasi_projective subvariety ??? ......

?? "domain of definition" of partially-defined multiplication operation on [projective line]^n .... ??? ....

?? "don't allow both 0 and infinity together" ??? ...... ???? ....... ?? vacuous for n=0 and n=1 ... ??? ...

?? sub-fan ?? .... ??? closure (... ?? ...) of just the two "constant" orthants ??? .... ?? two affine pieces glued together along torus ... ??? those two affine pieces being the n-ary toric convolution correpondences of the two affine pieces of the projective line ??? .... ???? ...... hmmmmm ....... ????? ......

?? is this really going to work with quasiprojective correspondences .... ???? ....

ordinary tensor-comonoidal correspondences vs toric-convolution-comonoidal correspondences ... ??? ...

comonoidalness of composite of comonoidal correspondences ... ??? lax interchange map ??? .... snake / tail ... ??? .... ordinary vs toric ... ??? ....