Quillen-Segal algebras and Stable homotopy theory

Hugo Bacard


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


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