Quasi-unital ∞–categories

Harpaz, Yonatan

doi:10.2140/agt.2015.15.2303

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Quasi-unital $\infty$–categories

Yonatan Harpaz

Algebraic & Geometric Topology 15 (2015) 2303–2381

DOI: 10.2140/agt.2015.15.2303

Abstract

Inspired by Lurie’s theory of quasi-unital algebras we prove an analogous result for $\infty$ –categories. By constructing a suitable model category of non-unital complete Segal spaces, we show that the unital structure of an $\infty$ –category can be uniquely recovered from the underlying non-unital structure once suitable candidates for units have been identified. The main result of this paper can be used to produce a proof of the $1$ –dimensional cobordism hypothesis, as described in a forthcoming paper of the author.

Keywords

higher category theory, complete Segal spaces, units

Mathematical Subject Classification 2010

Primary: 55U35, 55U40

References

Publication

Received: 11 June 2014

Revised: 30 October 2014

Accepted: 25 November 2014

Published: 10 September 2015

Authors

Yonatan Harpaz
Département de mathématiques et applications École Normale Supérieure 45 rue d’Ulm 75005 Paris France
http://sites.google.com/site/yonatanharpaz/

Volume 15, issue 4 (2015)