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arXiv · 2011.12723

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

Yonatan Harpaz·Joost Nuiten·Matan Prasma
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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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BibTeXRIS

Yonatan Harpaz, Joost Nuiten, Matan Prasma. 2020-11-25. On k-invariants for $(\infty, n)$-categories. https://doi.org/10.2140/agt.2025.25.721

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