  Let $\mathscr{M}$ be a monoidal model category that is also combinatorial and
left proper. If $\mathscr{O}$ is a monad, operad, properad, or a PROP;
following Segal's ideas we develop a theory of Quillen-Segal
$\mathscr{O}$-algebras and show that we have a Quillen equivalence between
usual $\mathscr{O}$-algebras and Quillen-Segal algebras. We use this theory to
get the stable homotopy category by a similar method as Hovey.
