  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.
