ScalingStacks

Theorem 4.4. The functor $\Gammac:\Space_{B}\rightarrow\Fun^{\otimes}(\mfld_{n}^{B},\Space)$ restricts as a fully faithful functor

$$\Space_{B}^{\geq n}~\hookrightarrow~\mathbf{H}(\mfld_{n}^{B},\Space)$$

from $n$-connective retractive spaces over $B$ to homology theories. The essential image consists of those $\mathcal{F}$ for which the restriction $\mathcal{F}_{|\disk_{n}^{B}}$ is group-like.