PreprintarXiv licencearXiv
Elmendorf's Theorem for ∞-categories
Abstract
Motivated by Teleman's study of gauged topological quantum field theories, our main result is an analog of Elmendorf's theorem in the setting of simplicial group actions on ∞-categories. In particular, we prove that if G is a simplicial group, there is a Quillen equivalence between the homotopy category of ∞-categories with G-action and the homotopy category of ∞-category-valued presheaves on the orbit category of G. We also show an analog of Whitehead's theorem in this setting.
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BibTeX
@misc{rowley2026elmendorfs,
title = {{Elmendorf's Theorem for $\infty$-categories}},
author = {Peter Rowley},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33183},
eprint = {2610.33183},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33183},
}
RIS
TY - UNPB
TI - Elmendorf's Theorem for ∞-categories
AU - Peter Rowley
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33183
UR - https://arxiv.org/abs/2610.33183
AB - Motivated by Teleman's study of gauged topological quantum field theories, our main result is an analog of Elmendorf's theorem in the setting of simplicial group actions on ∞-categories. In particular, we prove that if G is a simplicial group, there is a Quillen equivalence between the homotopy category of ∞-categories with G-action and the homotopy category of ∞-category-valued presheaves on the orbit category of G. We also show an analog of Whitehead's theorem in this setting.
ER -