A morphism of intersection homology induced by an algebraic map

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Let f:X-->Y be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups f*:IH*(Y)-->IH*(X) compatible with the induced homomorphism on cohomology. The crucial point in the argument is reduction to the finite characteristic. We give an alternative and short proof of the existence of a homomorphism f*. Our construction is an easy application of the Decomposition Theorem.