ScalingStacks

Remark 9.42. These definitions are consistent with the those of $m$ and $\ell$ of [33] in the case of a ringlike $A_{\infty}$ space of [33] — one can construct equivalences $\Omega^{\infty}MR\simeq m(\Omega^{\infty}R)$ and $\Omega^{\infty}LR\simeq\ell(\Omega^{\infty}R)$, although we leave the details to the interested reader, in order avoid a detailed discussion of the technology for $A_{\infty}$ ring spaces.