Abstract
In this note we give a precise definition of fully extended topological field theories à 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 and the cobordism bicategory from it.