Segal spaces, spans, and semicategories

We show that Segal spaces, and more generally category objects in an $infty$-category $mathcal{C}$, can be identified with associative algebras in the double $infty$-category of spans in $mathcal{C}$. We use this observation to prove that having identities is a property of a non-unital $(infty,n)$-category.