??? given an element of the co-fan lattice .... consider .... translating by it .... as an attempted map from .... ???? the unit toric quasicoherent sheaf to .... invertible quasicoherent sheaf obtained by ..... ?????

???? relationship to ..... ????morphisms in cocone category as translations .... ???? .....

??? morphisms between cocones vs morphisms between line bundles ..... ????? ....