On k-invariants for (∞,n)-categories

Harpaz, Yonatan; Nuiten, Joost; Prasma, Matan

doi:10.2140/agt.2025.25.721

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

Yonatan Harpaz, Joost Nuiten and Matan Prasma

Algebraic & Geometric Topology 25 (2025) 721–790

DOI: 10.2140/agt.2025.25.721

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 system for spaces. Our proof relies on an abstract analysis of Postnikov-type systems equipped with $k$ -invariants, and also yields a construction of $k$ -invariants for algebras over $\infty$ -operads and enriched $\infty$ -categories.

Keywords

Postnikov tower, $k$-invariants, higher categories

Mathematical Subject Classification

Primary: 18N65, 55S45

References

Publication

Received: 28 March 2022

Revised: 25 November 2023

Accepted: 22 January 2024

Published: 16 May 2025

Authors

Yonatan Harpaz
Laboratoire Analyse, Géométrie et Applications CNRS & Université Sorbonne Paris Nord Villetaneuse France

Joost Nuiten
Institut de Mathématiques de Toulouse Université Toulouse III - Paul Sabatier Toulouse France

Matan Prasma
Ethereum Foundation Berlin Germany

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Volume 25, issue 2 (2025)