Let $M$ be a simplicial combinatorial model category.
Is there a right induced model structureright induced model structure on commutative monoids in $M$ under reasonabereasonable conditions?
If $M$ is the Kan-Quillen model structure on simplicial sets, there is a such a model structure, more generally for algebras over any Lawvere theory.
I am interested in more general situations, for example $M$ the model structure for Segal spaces.