ScalingStacks

Definition 4.1. For a space $B$, the $\infty$-category $\Space_{B}$ is that of retractive spaces over $B$. The $\oo$-category $\Space^{\geq n}_{B}$ is the full $\oo$-subcategory of $\Space_{B}$ consisting of those $X\rightleftarrows B$ for which the retraction is $n$-connective, that is, $\pi_{*}X\rightarrow\pi_{*}B$ is an isomorphism for $*<n$ with any choice of base-point of $B$.