Résumé
Algebr. Geom. Topol. 19 (2019) 533-655 In this extended 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$n\operatorname{Cob}$and the cobordism bicategory$n\operatorname{Cob}^{ext}$from it.