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

Joost Nuiten; Matan Prasma; Yonatan Harpaz

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

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arxiv 2011.12723 v1 pith:L463WW4T submitted 2020-11-25 math.AT math.CT

Yonatan Harpaz , Joost Nuiten , Matan Prasma This is my paper · ORCID

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keywords inftyk-invariantscategoriestowerabstractalgebrasanalogouslyanalysis

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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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Deformation Theory for $(\infty,n)$-categories
math.CT 2025-04 conditional novelty 7.0 of 10

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.

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