Quasi-unital $\infty$-Categories

Yonatan Harpaz (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

Inspired by Lurie's theory of quasi-unital algebras we prove an analogous result for $\infty$-categories. In particular, 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 for the 1-dimensional cobordism hypothesis, as described in a forthcoming paper.

Domaines: Topologie algébrique [math.AT]

Yonatan Harpaz. Quasi-unital $\infty$-Categories. Algebraic and Geometric Topology, 2015. ⟨hal-02409245⟩