A TranMap is a Mapping which combines the forward transformation of a supplied Mapping with the inverse transformation of another supplied Mapping, ignoring the un-used transformation in each Mapping (indeed the un-used transformation need not exist).
When the forward transformation of the TranMap is referred to, the transformation actually used is the forward transformation of the first Mapping supplied when the TranMap was constructed. Likewise, when the inverse transformation of the TranMap is referred to, the transformation actually used is the inverse transformation of the second Mapping supplied when the TranMap was constructed.
AST A Library for Handling World Coordinate Systems in Astronomy