2025/06/12 by Connor Malin, Malin, Connor
Decision Sciences · #18F50 #Advanced Bandit Algorithms Research #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Multi-Criteria Decision Making #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2506.11245
openalex publication_date 2025/06/12 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
A stable ∞-category is 1-semiadditive if the norms for all finite group actions are equivalences. In the presence of 1-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two variants of 1-semiadditivity for an ∞-category C and study their relation to the Goodwillie calculus of functors C → \s(C). We demonstrate that these variations of 1-semiadditivity are complete obstructions to the problem of endowing ∂_∗ F with either a right module or a divided power right module structure which completely classifies the Goodwillie tower of F. We find applications to algebraic localizations of spaces, the Morita theory of operads, and bar-cobar duality of algebras. Along the way, we address several milestones in these areas including: Lie structures in the Goodwillie calculus of spaces, spectral Lie algebra models of vh-periodic homotopy theory, and the Poincaré/Koszul duality of Ed-algebras.