ScalingStacks

Definition 9.41. Let $R$ be a connective $A_{\infty}$ ring spectrum. We set

$$MR=\colim_{n}\mathrm{Map}_{R}(R^{\lor n},R^{\lor n}),$$

the nonunital $A_{\infty}$ ring spectrum of finite $R$-valued matrices. We write $LR$ for the $A_{\infty}$ ring spectrum of locally finite matrices, i.e. the connective $A_{\infty}$ ring spectrum obtained as the homotopy pullback

where here $H$ denotes the Eilenberg-Mac Lane spectrum functor.