On k-invariants for (∞,n)-categories

Harpaz, Yonatan¹ ; Nuiten, Joost² ; Prasma, Matan³

¹Laboratoire Analyse, Géométrie et Applications, CNRS & Université Sorbonne Paris Nord, Villetaneuse, France
²Institut de Mathématiques de Toulouse, Université Toulouse III - Paul Sabatier, Toulouse, France
³Ethereum Foundation, Berlin, Germany

Algebraic and Geometric Topology, Tome 25 (2025) no. 2, pp. 721-790

Résumé

Every (∞,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 ∞-operads and enriched ∞-categories.

Détail

DOI : 10.2140/agt.2025.25.721

Keywords: Postnikov tower, $k$-invariants, higher categories

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