The Homotopy Theory of \einf Algebras
Michael A. Mandell
Let $k$ be a commutative ring and let $\oC$ be the operad of
differential graded $k$-modules obtained as the singular $k$-chains of
the linear isometries operad \cite[\S V.9]{km}. We show that the
category of $\oC$-algebras is a proper closed model category. We use
the amenable description of the coproduct in this category
\cite[V.3.4]{km} to analyze the coproduct of and develop a homotopy
theory for algebras over an arbitrary \einf operad.