  This paper develops a concept of relative Cauchy evolution for the class of
homotopy algebraic quantum field theories (AQFTs) that are obtained by
canonical commutation relation quantization of Poisson chain complexes. The key
element of the construction is a rectification theorem proving that the
homotopy time-slice axiom, which is a higher categorical relaxation of the
time-slice axiom of AQFT, can be strictified for theories in this class. The
general concept is illustrated through a detailed study of the relative Cauchy
evolution for the homotopy AQFT associated with linear Yang-Mills theory, for
which the usual stress-energy tensor is recovered.
