  Let f : X -> Y be a morphism between normal complex varieties, and assume
that Y is Kawamata log terminal. Given any differential form, defined on the
smooth locus of Y, we construct a "pull-back form" on X. The pull-back map
obtained by this construction is O_Y-linear, uniquely determined by natural
universal properties and exists even in cases where the image of f is entirely
contained in the singular locus of the target variety Y.
  One relevant setting covered by the construction is that where f is the
inclusion (or normalisation) of the singular locus of Y. As an immediate
corollary, we show that differential forms defined on the smooth locus of Y
induce forms on every stratum of the singularity stratification. The same
result also holds for many Whitney stratifications.
