  We define extension $\infty$-categories for exact $\infty$-categories in
terms of bifibrations. Extension $\infty$-categories are invariant when passing
to the stable hull, and consequently we show that they form an
$\Omega$-spectrum, generalizing a theorem of Retakh. Finally, we show that the
homotopy groups of extension $\infty$-categories are naturally isomorphic to
the higher extension groups of the extriangulated category given by the
homotopy category.
