#### Volume 14, issue 5 (2014)

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Homotopical resolutions associated to deformable adjunctions

### Andrew J Blumberg and Emily Riehl

Algebraic & Geometric Topology 14 (2014) 3021–3048
##### Abstract

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.

##### Keywords
derived functors, resolutions, Quillen adjunctions, homotopical functors
##### Mathematical Subject Classification 2010
Primary: 55U35
Secondary: 18G55, 18G10