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

A theorem of Retakh for exact $\infty$-categories and higher extension functors