Over a monoidal model category, under some mild assumptions, we equip the
categories of colored PROPs and their algebras with projective model category
structures. A Boardman-Vogt style homotopy invariance result about algebras
over cofibrant colored PROPs is proved. As an example, we define homotopy
topological conformal field theories and observe that such structures are
homotopy invariant.
Over a monoidal model category, under some mild assumptions, we equip the
categories of colored PROPs and their algebras with projective model category
structures. A Boardman-Vogt style homotopy invariance result about algebras
over cofibrant colored PROPs is proved. As an example, we define homotopy
topological conformal field theories and observe that such structures are
homotopy invariant.