The homotopy theory of representations of nets of algebras over a (small)
category with values in a closed symmetric monoidal model category is
developed. We illustrate how each morphism of nets of algebras determines a
change-of-net Quillen adjunction between the model categories of net
representations, which is furthermore a Quillen equivalence when the morphism
is a weak equivalence. These techniques are applied in the context of homotopy
algebraic quantum field theory with values in cochain complexes. In particular,
an explicit construction is presented that produces constant net
representations for Maxwell $p$-forms on a fixed oriented and time-oriented
globally hyperbolic Lorentzian manifold.
