Lemma 3.25 (0N4K) · ScalingStacks

0N4K

Lemma 3.25. For $G:\mathcal{V}\rightarrow\mathcal{V}^{\prime}$ a symmetric monoidal functor between $\otimes$ -presentable $\infty$ -categories whose restriction to underlying $\infty$ -categories preserves geometric realizations, there is a canonical equivalence $\int\circ G\xrightarrow{\simeq}G\circ\int$ of functors $\Alg_{\disk_{n}^{B}}(\mathcal{V})\rightarrow\Fun^{\otimes}(\mfld_{n}^{B},\mathcal{V}^{\prime})$ .

0N4L

Proof. The two functors agree on disjoint unions of Euclidean spaces, so it suffices to check that $G\int A$ is a homology theory with values in $\mathcal{V}^{\prime}$ . This is immediate by the assumption on $G$ . ∎

David Ayala, John Francis

Original source: arXiv:1206.5522v6