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- W2982181508 abstract "We study completion with respect to the iterated suspension functor on $mathcal{O}$-algebras, where $mathcal{O}$ is a reduced operad in symmetric spectra. This completion is the unit of a derived adjunction comparing $mathcal{O}$-algebras with coalgebras over the associated iterated suspension-loop homotopical comonad via the iterated suspension functor. We prove that this derived adjunction becomes a derived equivalence when restricted to 0-connected $mathcal{O}$-algebras and $r$-connected $tilde{Sigma}^r tilde{Omega}^r$-coalgebras. We also consider the dual picture, using iterated loops to build a cocompletion map from algebras over the iterated loop-suspension homotopical monad to $mathcal{O}$-algebras. This is the counit of a derived adjunction, which we prove is a derived equivalence when restricting to $r$-connected $mathcal{O}$-algebras and $0$-connected $tilde{Omega}^r tilde{Sigma}^r$-algebras." @default.
- W2982181508 created "2019-11-01" @default.
- W2982181508 creator A5037578971 @default.
- W2982181508 date "2019-10-28" @default.
- W2982181508 modified "2023-09-27" @default.
- W2982181508 title "Iterated delooping and desuspension of structured ring spectra" @default.
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