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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 ∞–categories. By constructing a suitable model category of non-unital complete Segal spaces, we show that the unital structure of an ∞–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/