Homotopy Algebras are Homotopy Algebras

Abstract

We prove that strongly homotopy algebras (such as $A_{\infty }$, $C_{\infty }$, sh Lie, $B_{\infty }$, $G_{\infty }$,...) are homotopically invariant in the category of chain complexes. An important consequence is a rigorous proof that `strongly homotopy structures transfer over chain homotopy equivalences.'

LaTeX 2.09, 31 pages, article 12pt + bezier, substantially revised