  In the case of a compact orientable pseudomanifold, a well-known theorem of
M. Goresky and R. MacPherson says that the cap product with a fundamental class
factorizes through the intersection homology groups. In this work, we show that
this classical cap product is compatible with a cap product in intersection
(co)-homology, that we have previously introduced. If the pseudomanifold is
also normal, for any commutative ring of coefficients, the existence of a
classical Poincar\'e duality isomorphism is equivalent to the existence of an
isomorphism between the intersection homology groups corresponding to the zero
and the top perversities.
