Pull-back morphisms for reflexive differential forms

Let f:X→Y be a morphism between normal complex varieties, where Y is Kawamata log terminal. Given any differential form σ, defined on the smooth locus of Y, we construct a “pull-back form” on X. The pull-back map obtained by this construction is 풪Y-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 Y.One relevant setting covered by the construction is that where f is the inclusion (or normalisation) of the singular locus Ysing. 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.