For every (∞,n)-category E, the stabilization of its slice category is equivalent to spectrum-valued functors on a twisted arrow category TwAr(E), yielding a deformation theory and a characterization of lax-idempotent monads.
On k-invariants for $(\infty, n)$-categories
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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.
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2025 1verdicts
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Deformation Theory for $(\infty,n)$-categories
For every (∞,n)-category E, the stabilization of its slice category is equivalent to spectrum-valued functors on a twisted arrow category TwAr(E), yielding a deformation theory and a characterization of lax-idempotent monads.