In the case that for ∞Grpd we say that
the cohomology of with constant coefficients, constant on
For the (∞,1)-sheaf (∞,1)-topos over an (∞,1)-site , we have that is the constant ∞-stack over . Notice that this is the ∞-stackification of the (∞,1)-presheaf that is literally constant (as an (∞,1)-functor) on . So unless over constant presheaves already satisfy descent (as for instance over an (∞,1)-cohesive site) the object is not itself given by a constant functor on .
then by the adjunction hom-equivalence we have that cohomology with constant coefficients in is equivalently the cohomology of the fundamental ∞-groupoid in a locally ∞-connected (∞,1)-topos in ∞Grpd with coefficients in .
in this cohomology may then be identified with what is called a local system on with coefficients in . So in this case we have