  Cofibrations are defined in the category of Fr\"olicher spaces by weakening
the analog of the classical definition to enable smooth homotopy extensions to
be more easily constructed, using flattened unit intervals. We later relate
smooth cofibrations to smooth neighborhood deformation retracts. The notion of
smooth neighborhood deformation retract gives rise to an analogous result that
a closed Fr\"olicher subspace $A$ of the Fr\"olicher space $X$ is a smooth
neighborhood deformation retract of $X$ if and only if the inclusion $i:
A\hookrightarrow X$ comes from a certain subclass of cofibrations. As an
application we construct the right Puppe sequence.
