Homotopy theory of modules over operads in symmetric spectra

By John E. Harper. 2007

55 citations recorded by the source corpus.

We establish model category structures on algebras and modules over operads in symmetric spectra and study when a morphism of operads induces a Quillen equivalence between corresponding categories of algebras (resp. modules) over operads.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7313731348712c9a25103c0d5b9635aa85e9520e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. David White
2. Kathryn Hess
3. Jakob Scholbach
4. D. Pavlov
5. John E. Harper

In Geometry and Topology

1. David White
2. Kathryn Hess
3. Jakob Scholbach
4. D. Pavlov
5. John E. Harper

In Mathematical Physics

1. David White
2. Kathryn Hess
3. Jakob Scholbach
4. D. Pavlov
5. John E. Harper

Citations in the corpus

• Admissibility and rectification of colored symmetric operads (2014, background): “Harper showed the admissibility of all symmetric operads in simplicial symmetric spectra [22].”
• Homotopy completion and topological Quillen homology of structured ring spectra (2011, methodology): “Our approach to this generalization, which is motivated by Hornbostel [37], is to establish only the necessary minimum of technical propositions for Rmodules needed for the proofs of the main results as described in [31, 32] to remain valid in the more general context of R-modules.”
• Model structures on commutative monoids in general model categories (2014, methodology): “onomorphisms for all n. Similarly, Lemma 8.3.2(2) of [56] implies that Symn(g) is a weak equivalence for all n. These two results are special cases of Proposition 4.28∗(b) and Proposition 4.29∗(a) in [18] (corrigendum). In the notation of [56], B should be taken to be the monoidal unit S with the tr”