A note on the (∞,n)–category of cobordisms

  title={A note on the (∞,n)–category of cobordisms},
  author={Damien Calaque and Claudia I. Scheimbauer},
  journal={Algebraic \& Geometric Topology},
In this 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 and the cobordism bicategory from it. 

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