  Every $(\infty, n)$-category can be approximated by its tower of homotopy
$(m, n)$-categories. In this paper, we prove that the successive stages of this
tower are classified by k-invariants, analogously to the classical Postnikov
tower for spaces. Our proof relies on an abstract analysis of Postnikov-type
towers equipped with k-invariants, and also yields a construction of
k-invariants for algebras over $\infty$-operads and enriched
$\infty$-categories.
