Model Structures on Commutative Monoids in General Model Categories
نویسنده
چکیده
We provide conditions on a monoidal model categoryM so that the category of commutative monoids in M inherits a model structure from M in which a map is a weak equivalence or fibration if and only if it is so inM. We then investigate properties of cofibrations of commutative monoids, rectification between E∞-algebras and commutative monoids, the relationship between commutative monoids and monoidal Bousfield localization functors, when the category of commutative monoids can be made left proper, and functoriality of the passage from a commutative monoid R to the category of commutative Ralgebras. In the final section we provide numerous examples of model categories satisfying our hypotheses.
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