Let X and Y be normal toric varieties whose underlying lattices are NX and NY respectively. A toric map is a morphism f : X →Y that induces a morphism of algebraic groups g : TX →TY such that f is TX-equivariant with respect to the TX-action on Y induced by g. Every toric map f : X →Y corresponds to a unique map fN : NX →NY between the underlying lattices such that, for every cone σ in the fan of X, there is a cone in the fan of Y that contains the image fN(σ). For details see Theorem 3.3.4 in Cox-Little-Schenck.
To specify a map of normal toric varieties, the target and source normal toric varieties need to be specificied as well as a matrix which maps from NX to NY.
The primary constructor of a toric map is map(NormalToricVariety,NormalToricVariety,Matrix).