  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.
