2025/06/12 by Shai Keidar, Keidar, Shai, Shaul Ragimov +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2506.11240
Given a presentably symmetric monoidal ∞-category C and an 𝔼∞-monoid M, we introduce and classify twisted graded categories, which generalize the Day convolution structure on Fun(M, C). These are characterized by a braiding encoded in symmetric group actions on tensor powers, whose character we show depends only on the \mathbbT-equivariant monoidal dimension. We analyze the \mathbbT-action on the dimension of invertible objects and identify it with the \mathbbT-transfer map. Finally, we compute braiding characters in examples arising from higher cyclotomic extensions, such as the (\mathbbS, n+1)-oriented extension of ModEn\wedge at all primes and heights, and of the cyclotomic closure of Vectn at low heights.