Defining a Derivative Operator to Kill It Off

We know that d a composed with itself is going to be the curvature, and we want that to be hit by a cab operator. So you want something like f a followed by chib over here to cancel. Then you think, okay, well how am i going to get at getting this augmented torsion? And then you realize that the information in the now homogeneous gage group, you actually have information not for one connection, but for two connections.