Exercise 10, § 1

Suppose that K is a $\mathbf{Q}$-algebra. Let E be a cocommutative K-bigebra with a filtration compatible with its bigebra structure. Show that the morphism

defined in no. 4, Proposition 8 is an isomorphism, if $P(E)$ is assumed to be a free K-module (same proof as for Theorem 1).