on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
representation, ∞-representation?
symmetric monoidal (∞,1)-category of spectra
Let
$\mathcal{E}$ be a cofibrantly generated symmetric monoidal model category;
$P$ an admissible $\Sigma$-cofibrant operad in $\mathcal{E}$ (see model structure on operads);
$A$ a cofibrant $P$-algebra (see model structure on algebras over an operad).
Then then category $Mod_P(A)$ of modules over an algebra over an operad carries the transferred model structure along the forgetful functor $U : Mod_P(A) \to \mathcal{E}$.
Every morphism of cofibrant $P$-algebras $f : A \to B$ induced a Quillen adjunction
which is a Quillen equivalence if $f$ is a weak equivalence.
This is (BergerMoerdijk, theorem 2.6).
(∞,1)-operad, model structure on operads
algebra over an (∞,1)-operad, model structure on algebras over an operad
Last revised on February 11, 2013 at 01:36:37. See the history of this page for a list of all contributions to it.