Hi, was hoping someone could provide some pointers on a simple question. In 1.1.2.17 Of higher algebra, Lurie seems to say there is a construction of a "mapping spectrum" In a stable infinity category. What is this construction? Is it written down somewhere?

@Bbb I'm not sure what level of technical detail you are looking for but it comes from the fact that the loop functor is an equivalence. Let $X$ and $Y$ be objects in a stable infinity category. Then we can define an $\Omega$ spectrum by setting $Z_n = Map(X, \Sigma^n Y)$. Its naturally an $\Omega$ spectrum via the equivalences $\Omega Z_{n+1} = \Omega Map(X, \Sigma^{n+1} Y) = Map(\Sigma X, \Sigma^{n+1} Y) = Map(X, \Omega \Sigma^n Y) = Map(X, \Sigma^n Y) = Z_n$.

Ah that makes perfect sense, thanks!