 In order to remedy this, one defines in this situation for a sheaf of formula_30-modules formula_31 its inverse image by

However, the morphisms formula_42 and formula_43 are "almost never" isomorphisms.For example, if formula_47 denotes the inclusion of a closed subset, the stalk of formula_48 at a point formula_49 is canonically isomorphic to formula_50 if formula_20 is in formula_52 and formula_53 otherwise.A similar adjunction holds for the case of sheaves of modules, replacing formula_54 by formula_55.