Keller sequences of exact $\infty$-categories

Yonatan Harpaz; Daniel Marlowe

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arXiv · 2609.01473

Keller sequences of exact $\infty$-categories

Yonatan Harpaz·Daniel Marlowe

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Abstract

We study a family of fibre-cofibre sequences in the $\infty$-category of exact $\infty$-categories, which we call Keller sequences, generalising the notion of Verdier sequences of stable $\infty$-categories. We show that algebraic K-theory is localising with respect to this family, and use this to give a categorical proof of Quillen's resolution theorem. Our arguments hinge upon a mapping space characterisation of special inclusions as studied by Keller, from which we deduce another proof of Keller's theorem that such inclusions induce fully faithful functors on stable envelopes.

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Yonatan Harpaz, Daniel Marlowe. 2026-09-01. Keller sequences of exact $\infty$-categories. https://arxiv.org/abs/2609.01473

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