Koszul exterior connections

Question

Let $(E,M)$ be a vector bundle over the riemannian manifold $(M,g)$ which is a module for the exterior algebra of $M$. A Koszul exterior connection $\nabla$ is an operator such that:

$$\nabla : E \rightarrow \Lambda^* (TM) \otimes_{{\cal C}^{\infty}(M)} E$$

$$\nabla_{\alpha} f.s= df^* (\alpha)\wedge s + f .\nabla_{\alpha} s$$

With $\alpha$ an exterior form, $f$ a smooth function of $M$, and $s$ a section of $E$.

What is the space of Koszul exterior connections?