A toric map is a morphism $f : X \to Y$ between normal toric varieties that induces a morphism of algebraic groups $g : T_X \to T_Y$ such that $f$ is $T_X$-equivariant with respect to the $T_X$-action on $Y$ induced by $g$. Every toric map $f : X \to Y$ corresponds to a unique map $f_N : N_X \to N_Y$ between the underlying lattices.

Although the primary method for creating a toric map is map(NormalToricVariety,NormalToricVariety,Matrix), there are a few other constructors.

- map(NormalToricVariety,NormalToricVariety,Matrix) -- make a torus-equivariant map between normal toric varieties
- id _ NormalToricVariety -- make the identity map from a NormalToricVariety to itself
- NormalToricVariety ^ Array -- make a canonical projection map
- NormalToricVariety _ Array -- make a canonical inclusion into a product
- diagonalToricMap -- make a diagonal map into a Cartesian product
- ToricMap -- the class of all torus-equivariant maps between normal toric varieties
- isWellDefined(ToricMap) -- whether a toric map is well defined

Having made a toric map, one can access its basic invariants or test for some elementary properties by using the following methods.

- source(ToricMap) -- get the source of the map
- target(ToricMap) -- get the target of the map
- matrix(ToricMap) -- get the underlying map of lattices
- ToricMap * ToricMap -- make the composition of two toric maps
- isProper(ToricMap) -- whether a toric map is proper
- isFibration(ToricMap) -- whether a toric map is a fibration
- isDominant(ToricMap) -- whether a toric map is dominant
- isSurjective(ToricMap) -- whether a toric map is surjective

Several functorial aspects of normal toric varieties are also available.

- weilDivisorGroup(ToricMap) -- make the induced map between groups of Weil divisors
- classGroup(ToricMap) -- make the induced map between class groups
- cartierDivisorGroup(ToricMap) -- make the induced map between groups of Cartier divisors.
- picardGroup(ToricMap) -- make the induced map between Picard groups
- pullback(ToricMap,ToricDivisor) -- make the pullback of a Cartier divisor under a toric map
- pullback(ToricMap,CoherentSheaf) -- make the pullback of a coherent sheaf under a toric map
- inducedMap(ToricMap) -- make the induced map between total coordinate rings (a.k.a. Cox rings)
- ideal(ToricMap) -- make the ideal defining the closure of the image

- finding attributes and properties -- information about accessing features of a normal toric variety
- working with divisors -- information about toric divisors and their related groups
- working with sheaves -- information about coherent sheaves and total coordinate rings (a.k.a. Cox rings)
- resolving singularities -- information about find a smooth proper birational surjection