Model structures on commutative monoids in general model categories
By David White. 2014
64 citations recorded by the source corpus.
Abstract We provide conditions on a monoidal model category M 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 in M . 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 R -algebras. In the final section we provide numerous examples of model categories satisfying our hypotheses.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/19fa751d597380096e770420abcfe1ad533a130c
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Admissibility and rectification of colored symmetric operads (2014, result): “utative monoids. The admissibility of the commutative operad was shown by Lurie [Lur] under a strong assumption on C, which was then relaxed to a condition similar to symmetric i-monoidality by White [Whi14a]. The admissibility of all operads was shown by Elmendorf and Mandell for C= sSet [EM06, The”
- Global Homotopy Theory (2018, background): “2 of [188] thus shows that the positive global model structure of orthogonal spectra lifts to a cofibrantly generated model structure on the category of ultra-commutative ring spectra.”