2025/01/23 by Merlin Christ, Christ, Merlin · 1 citation
Computer Science · Decision Sciences · Mathematics · #16E45 #18N60 #Advanced Algebra and Logic #Algebra over a field #Algebraic Topology (math.AT) #Categorical variable #Combinatorics #Computer science #Cyclic group #FOS: Mathematics #Fuzzy and Soft Set Theory #Group (periodic table) #Mathematics #Physics #Pure mathematics #Quotient #Quotient group #Representation Theory (math.RT) #Rings, Modules, and Algebras #Skew #Statistics
paper · pdf · doi:10.48550/arxiv.2501.13666
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We relate group quotients of dg-categories and linear stable ∞-categories. Given a group acting on a dg-algebra, we prove that the skew group dg-algebra is Morita equivalent to the dg-categorical homotopy group quotient. We also treat the cases of group actions on dg-categories, with corresponding skew group dg-categories, and of orbit dg-categories. Finally, we describe a version of the skew group algebra in the setting of ring spectra and relate it with ∞-categorical group quotients.