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Keywords:
homotopy algebras; operads; spectra; Segal categories; $\infty$-categories
Summary:
Let $\scr M$ be a monoidal model category that is also combinatorial. If $\scr O$ is a monad, operad, properad, or a PROP; following Segal’s ideas we develop a theory of Quillen-Segal $\scr O$-algebras and show that we have a Quillen equivalence between usual $\scr O$-algebras and Quillen-Segal $\scr O$-algebras. We also introduce Quillen-Segal theories and we use them to obtain the stable homotopy category by a similar method to that of Hovey.
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