On k-invariants for $(\infty ,n)$-categories

Abstract

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.

References in corpus (1)

• The abstract cotangent complex and Quillen cohomology of enriched categories