ScalingStacks

Definition 6.4. Let ${\rm Bord}_{\rm Spaces}$ denote the bordism $(\infty,1)$-category of spaces, with 1-morphisms from $U$ to $V$ given by spaces $T_{UV}$ with maps $U\rightarrow T_{UV}\leftarrow V$, and composition of $T:U\to V$ and $T^{\prime}:V\to W$ given by the homotopy pushout of spaces

$$T^{\prime}\circ T=T\amalg_{V}T^{\prime}.$$

We endow ${\rm Bord}_{\rm Spaces}$ with a symmetric monoidal structure given by disjoint union.