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Homotopical resolutions
associated to deformable adjunctions
Andrew J Blumberg and Emily Riehl |
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Algebraic & Geometric Topology 14 (2014) 3021–3048
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Abstract |
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Given an adjunction 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
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Mathematical Subject Classification 2010
Primary: 55U35
Secondary: 18G55, 18G10
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References |
Publication
Received: 26 October 2013
Revised: 5 February 2014
Accepted: 15 February 2014
Published: 5 November 2014
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Authors |
| Andrew J Blumberg | |
| Department of Mathematics The University of Texas RLM 8.100 2515 Speedway Stop C1200 Austin, TX 78712 USA |
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| https://www.ma.utexas.edu/users/blumberg/ | |
| Emily Riehl | |
| Department of Mathematics Harvard University 1 Oxford Street Cambridge, MA 02138 USA |
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| http://www.math.harvard.edu/~eriehl | |
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