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arXiv · 2512.12263

Categorified Koszul duality of algebras

Isamu Iwanari
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Abstract

Koszul duality is a duality between algebras that provides deep connections between seemingly different algebraic objects and has important applications in various areas of mathematics. The classical form of Koszul duality concerns associative algebras. In this paper, we develop a categorified generalization of Koszul duality that treats duality phenomena among monoidal stable $\infty$-categories. In our framework, monoidal stable infinity-categories play the role of associative algebras in the classical theory. We establish Koszul duality results for module infinity-categories associated with Artin algebras and related algebras over the little 2-discs operad. The resulting duality exhibits several structural features, including connections to right and left complete t-structures and to categories of Ind-coherent modules.

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Isamu Iwanari. 2025-12-13. Categorified Koszul duality of algebras. https://arxiv.org/abs/2512.12263

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