PreprintCC BY 4.0HAL
Keller sequences of exact ∞-categories
Abstract
We study a family of fibre-cofibre sequences in the ∞-category of exact ∞-categories, which we call Keller sequences, generalising the notion of Verdier sequences of stable ∞-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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BibTeX
@misc{harpaz2026keller,
title = {{Keller sequences of exact ∞-categories}},
author = {Yonatan Harpaz and Daniel Marlowe},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01473},
eprint = {2609.01473},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05734807v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Keller sequences of exact ∞-categories
AU - Yonatan Harpaz
AU - Daniel Marlowe
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2609.01473
UR - https://hal.science/hal-05734807v1
AB - We study a family of fibre-cofibre sequences in the ∞-category of exact ∞-categories, which we call Keller sequences, generalising the notion of Verdier sequences of stable ∞-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.
ER -