We know given a Connection 1-form $\omega$ on a Principle bundle $P(M,G)$ we can define a curvature 2-form $\Omega$ of $\omega$. We also know that given a Connection 1-form $\omega$ we can define a Connection $\lambda$ (a smooth distribution on $P$) .

**My question is the following**:

Is there any equivalent notion of Curvature 2- form which arise from the notion (

when Connection is given as a smooth distribution on $P$) andindependentof the notion(Connection 1-form)? Since we already know that when a Connection is given as a distribution then we can define the notion ofParallel transportandHolonomy groupsindependent of the notion of Connection 1-form.Can we some way define the notion of Curvature in terms of Parallel transport and Holonomy groupsindependentof considering the corresponding connection 1-form of the given Connection so that "this" notion of curvature obtained inthisway will be equivalent to theour standard notion of Curvature 2-form of a Connection 1 -form?

I think **Ambrose-Singer Holonomy Theorem** relates partially the Curvature 2-form of a Connection form and the Holonomy of the corresponding Connection. Can it be used in some way to define alternative independent equivalent notion of Curvature of a Connection?