A note on the $(\infty,n)$-category of cobordisms

Understand

In this extended note we give a precise definition of fully extended topological field theories \`a la Lurie.

• Using complete $n$-fold Segal spaces as a model, we construct an $(\infty,n)$-category of $n$-dimensional cobordisms, possibly with tangential structure.
• We endow it with a symmetric monoidal structure and show that we can recover the usual category of cobordisms $n\operatorname{Cob}$ and the cobordism bicategory $n\operatorname{Cob}^{ext}$ from it.