2025/03/04 by Lenz, Tobias, Linskens, Sil, Pützstück, Phil · 3 citations
#18N60 (Secondary) #18N70 #55P43 (Primary) #55P91 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.02839
We show that the ∞-category of normed algebras in genuine G-spectra, as introduced by Bachmann-Hoyois, is modelled by strictly commutative algebras in G-symmetric spectra for any finite group G. We moreover provide an analogous description of Schwede's ultra-commutative global ring spectra in higher categorical terms. Using these new descriptions, we exhibit the ∞-category of ultra-commutative global ring spectra as a partially lax limit of the ∞-categories of genuine G-spectra for varying G, in analogy with the non-multiplicative comparison of Nardin, Pol, and the second author. Along the way, we establish various new results in parametrized higher algebra, which we hope to be of independent interest.