ScalingStacks

Definition 2.18. The ordinary symmetric monoidal category $\dmfld_{n}$ is that for which an object is a topological $n$-manifold, and a morphism is an open embedding between two such; composition is composition of maps, and the symmetric monoidal structure is given by disjoint union. Likewise, the ordinary symmetric monoidal category $\ddisk_{n}\subset\dmfld_{n}$ is the full subcategory consisting of those topological $n$-manifolds that are homeomorphic to a finite disjoint union of Euclidean spaces.