ScalingStacks

Definition 2.14. $\mfld_{n}^{\partial}$ is the symmetric monoidal topological category of topological $n$-manifolds, possibly with boundary, which have finite good covers by Euclidean spaces $\mathbb{R}^{n}$ and upper half spaces $\mathbb{R}_{\geq 0}\times\mathbb{R}^{n-1}$. Morphisms are open embeddings which map boundary to boundary. $\disk_{n}^{\partial}$ is the full symmetric monoidal topological subcategory of $\mfld_{n}^{\partial}$ consisting of finite disjoint unions of $\mathbb{R}^{n}$ and $\mathbb{R}_{\geq 0}\times\mathbb{R}^{n-1}$.