Homotopical resolutions associated to deformable adjunctions

Blumberg, Andrew J¹ ; Riehl, Emily²

¹Department of Mathematics, The University of Texas, RLM 8.100, 2515 Speedway Stop C1200, Austin, TX 78712, USA
²Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 3021-3048

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.3021

Classification : 55U35, 18G55, 18G10
Keywords: derived functors, resolutions, Quillen adjunctions, homotopical functors

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