English

Homotopical resolutions associated to deformable adjunctions

Algebraic Topology 2014-12-03 v2 Category Theory

Abstract

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

Cite

@article{arxiv.1208.2844,
  title  = {Homotopical resolutions associated to deformable adjunctions},
  author = {Andrew J. Blumberg and Emily Riehl},
  journal= {arXiv preprint arXiv:1208.2844},
  year   = {2014}
}

Comments

22 pages; v2 is the final journal version, with expository improvements suggested by the referee

R2 v1 2026-06-21T21:50:24.592Z