PreprintarXiv licencearXiv
A Categorical Approach to Nilspace Theory
Abstract
Originating in ergodic structure theory, nilspace theory is concerned with the study of cubical spaces. A first key result in this theory, the weak structure theorem, is the representation of a concrete fibrant compact cubespace as a tower of its canonical truncations, exhibiting each step over the previous one as a principal bundle by a compact abelian group. We present a categorical proof of the weak structure theorem by systematically interpreting the relevant concepts in an appropriate context.
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BibTeX
@misc{bihlmaier2026categorical,
title = {{A Categorical Approach to Nilspace Theory}},
author = {Noa Bihlmaier and Nick Ruoff},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10415},
eprint = {2609.10415},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10415},
}
RIS
TY - UNPB
TI - A Categorical Approach to Nilspace Theory
AU - Noa Bihlmaier
AU - Nick Ruoff
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10415
UR - https://arxiv.org/abs/2609.10415
AB - Originating in ergodic structure theory, nilspace theory is concerned with the study of cubical spaces. A first key result in this theory, the weak structure theorem, is the representation of a concrete fibrant compact cubespace as a tower of its canonical truncations, exhibiting each step over the previous one as a principal bundle by a compact abelian group. We present a categorical proof of the weak structure theorem by systematically interpreting the relevant concepts in an appropriate context.
ER -