??so consider TAG theory of toric quasicoherent sheaves over projective line ... ???... and consider ... ???models into TAG theory of k-modules vs into that of [mult monoid(k)]-sets ... ??? ....

??seems like they probably _are_ different in general ??? ... ?? "ideal class group vs toric ideal class group" ?? .... ???? ... ??? ...

??so maybe it really is true that ... in affine case they're the same, but pretty much not beyond that ... ????.... ??? ....

??analogy set : ab gp :: a-module : b-module here, for comm ring hom h : a -> b ?? ...

?? models of [a-AG theory of quasicoherent sheaves over projective line relative to a] into [a-AG theory of "k-modules over b" ???? .....] vs into [a-AG theory of "k-modules over a" ... ???? ...... ???? ...] .... ????

??having trouble seeing difference here??? .... ????work out more explicitly ??? ...

commutative ring k : commutative b-algebra k :: .... ????? .....


????square .... ???? ....

commutative monoidal ab gp .... comm monoidal set ....
ab gp .... set ....

??????? ...... ???? .....