In this extended note we give a precise definition of fully extended topological field theories à la Lurie. Using complete –fold Segal spaces as a model, we construct an –category of –dimensional bordisms, possibly with tangential structure. We endow it with a symmetric monoidal structure and show that we can recover the usual category of bordisms.
"A note on the $(\infty,n)$–category of cobordisms." Algebr. Geom. Topol. 19 (2) 533 - 655, 2019. https://doi.org/10.2140/agt.2019.19.533