Volume 15, issue 4 (2015)

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Quasi-unital $\infty$–categories

Yonatan Harpaz

Algebraic & Geometric Topology 15 (2015) 2303–2381
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