Some remarks on higher Morita categories

We take another look at the construction of double $\mathrm{\infty }$-categories of algebras and bimodules and prove a few supplemental results about these, including a simpler proof of the Segal condition and a comparison between our construction and that of Lurie. We then take a more streamlined, inductive approach to the higher Morita categories of $E_n$-algebras and show that these deloop correctly.