?? underlying toric quasicoherent sheaf of unit quasicoherent sheaf (?? wrt "ordinary" tensor product ...) over 1d torus ...

?? hmmm .... unit toric quasicoherent sheaf wrt "tensor product" .... corresponding (??? ....) quasicoherent sheaf ....... ?????? ....

?? unit quasicoherent sheaf wrt ordinary tensor product as comonoidal wrt toric convolution ??? ..... ???? ... ?? maybe contrary to something that i wrote the other day ?? ... ... ?? ...

?? still confusion here .... ??? ....

?? hmm, does that (?? namely, idea of ordinary unit being toric convolution comonoid ... ??? ...) conflict with "divergence" idea that we had ?? .... of hypothetical (?? ..) comultiplication .... ???? ....

?? laurent polynomials in x1, x2 as module over laurent polynomials in x ..... ?? ....

???? comonoidal reps of abelian lie alg ...... ?????? ..... ??? then specially nice such ??? ...... as forming accidental topos of correponding torus ..... ????? ....

?? did we accidentally perform some fourier duality flip here ????? .... ????? .... .... acting vs grading .... acting by lattice and grading by torus vs vice versa ...... ???? .....

???? hmmm, acting by lattice and grading by lattice do both enter here (?? ... ??? graded commutative monoid and sections of toric line bundles ... ??? ...) , right ???? .....

??? hmmm, lie algebra idea here as seeming to apply directly only to toruses and not to more general toric varieties ....... ????? ......

????? .....

?? ok, yes we made a silly duality flip here .... quasicoherent sheaf over torus as rep of lattice, not of torus ...

?? so in affine case, simply cocomm coalg acted on by lattice ,,, ??

?? more generally, simply cocomm coalg in accidental topos ... ?? ....

?? "spectrum" interpretation of toric quasicoherent sheaf here ... again ... ?? ... ??? case of ordinary unit ... ?? ....

?? "comultiplication divergence" idea here ??? .... ???? ....

?? these cocomm comonoid cats ... ?? as enriched over plain (...) cocomm comonoids .... ???? ....