A note on the (∞,n)-category of cobordisms

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 (∞,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 nCob and the cobordism bicategory nCobext from it