Homotopical resolutions associated to deformable adjunctions

Andrew J. Blumberg*, Emily Riehl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


Given an adjunction F ⊣ G connecting reasonable categories with weak equivalences, we define a new derived bar and cobar construction associated to the adjunction. This yields homotopical models of the completion and cocompletion associated to the monad and comonad of the adjunction. We discuss applications of these resolutions to spectral sequences for derived completions and Goodwillie calculus in general model categories.

Original languageEnglish
Pages (from-to)3021-3048
Number of pages28
JournalAlgebraic and Geometric Topology
Issue number5
Publication statusPublished - 6 Nov 2014
Externally publishedYes


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