Functor calculus completions for retractive operadic algebras in spectra

2024/07/01 by Matthew B. Carr, Carr, Matthew B., John E. Harper +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2407.01819

openalex publication_date 2024/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to study convergence of Bousfield-Kan completions with respect to the 1-excisive approximation of the identity functor and exotic convergence of the Taylor tower of the identity functor, for algebras over operads in spectra centered away from the null object. In Goodwillie's homotopy functor calculus, being centered away from the null object amounts to doing homotopy theory and functor calculus in the retractive setting.

Related

• Retractive spaces and Bousfield-Kan completions
• Operads and chain rules for the calculus of functors
• A classification of Taylor towers of functors of spaces and spectra
• Comparing the orthogonal and homotopy functor calculi
• The partition poset complex and the Goodwillie derivatives of the identity in spaces