  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.
