2020/02/05 by Glasman, Saul, Lawson, Tyler
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2002.02035
For any E_∞ ring spectrum E, we show that there is an algebra Pow(E) of stable power operations that acts naturally on the underlying spectrum of any E-algebra. Further, we show that there are maps of rings E → Pow(E) → End(E), where the latter determines a restriction from power operations to stable operations in the cohomology of spaces. In the case where E is the mod-p Eilenberg-Mac Lane spectrum, this realizes a natural quotient from Mandell's algebra of generalized Steenrod operations to the mod-p Steenrod algebra. More generally, this arises as part of a classification of endomorphisms of representable functors from an ∞-category C to spectra, with particular attention to the case where C is an O-monoidal ∞-category.