General Covariance from the Viewpoint of Stacks

General covariance is a crucial notion in the study of field theories on curved spacetimes. Roughly, a generally covariant field theory is one that is defined with respect to a background semi-Riemannian metric such that it is only sensitive to the diffeomorphism classes of that metric. In other words, the bundle of theories over the space of semi-Riemannian metrics is equivariant with respect to the diffeomorphism group of the underlying spacetime. In this talk, we will make the preceding ideas precise by using stacks and introducing examples.