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

@article{Calaque2019ANO,
title={A note on the (∞,n)–category of cobordisms},
author={Damien Calaque and Claudia I. Scheimbauer},
journal={Algebraic \& Geometric Topology},
year={2019}
}
• Published 29 September 2015
• Mathematics
• 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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