On Homotopy Invariance for Algebras over Colored PROPs

Mark W. Johnson and Donald Yau

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 \emph{homotopy} topological conformal field theories and observe that such structures are homotopy invariant.

Journal of Homotopy and Related Structures, Vol. 4(2009), No. 1, pp. 275-315