  We generalize the notion, introduced by Henri Cartan, of an operation of a
Lie algebra $\mathfrak g$ in a graded differential algebra $\Omega$. We define
the notion of an operation of a Hopf algebra $\mathcal H$ in a graded
differential algebra $\Omega$ which is refered to as a $\mathcal H$-operation.
We then generalize for such an operation the notion of algebraic connection.
Finally we discuss the corresponding noncommutative version of the Weil
algebra: The Weil algebra $W(\mathcal H)$ of the Hopf algebra $\mathcal H$ is
the universal initial object of the category of $\mathcal H$-operations with
connections.
