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

© 2019, Mathematical Sciences Publishers. All rights reserved. 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 (∞; n)–category of n–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.