10:17 AM
I want to understand the relation between tate construction and power operations. Fortunately there's this wonderful paper: http://www-users.math.umn.edu/~tlawson/papers/power.pdf

Unfortunately it assumes a familiarity with Equivariant homotopy which I unfortunately don't posses. What should I read to be better prepared for this paper? Or maybe there's a different reference which doesn't use too much equivariant stuff?

9 hours later…
6:50 PM
If $R$ is an $A_{\infty}$-algebra in spectra, then we have the stable $\infty$-category $Mod_{R}$ of $R$-modules, and its homotopy category $h Mod_{R}$ is canonically triangulated.
Is the triangulated category $h Mod_{R}$ determined by the underlying $A_{n}$-algebra for some finite $n$?

7:18 PM
@PiotrPstrągowski presumably the (n+epsilon)-category of potential n-stages for an R-module only depends on the A_{n+delta}-algebra structure of R? in which case, by your trick, you'd be okay in the event that R_* has finite cohomological dimension, right?

7:28 PM
as a sanity check, if we don't care about the triangulated structure, then we can define hMod_{K(n)} using essentially no information about the multiplicative structure on K(n) since every module over K(n)_* is free