ScalingStacks

After Corollary 2.4 we have a tangent classifier, functorial in a coherent homotopy sense, given by the restricted Yoneda functor:

(1)

$$\tau\colon\mfld_{n}\longrightarrow\Psh(\mfld_{n})\longrightarrow\Psh(\mathcal{E}{\sf uc}_{n})~\underset{\rm Cor~\ref{euc}}{\simeq}~\spaces_{/\BTop(n)}~.$$

We will postpone to Corollary 2.13 justification for this terminology. To define the $\infty$-category of $B$-framed $n$-manifolds as it is equipped with a symmetric monoidal structure, we record a few standard facts about $\infty$-categories together with an observation about the functor $\tau$.