Classifying spaces of algebras over a prop

We prove that a weak equivalence between cofibrant props induces
a weak equivalence between the associated classifying spaces of algebras. This
statement generalizes to the prop setting a homotopy invariance result which
is well known in the case of algebras over operads. The absence of model
category structure on algebras over a prop leads us to introduce new methods
to overcome this difficulty. We also explain how our result can be extended
to algebras over colored props in any symmetric monoidal model category
tensored over chain complexes.