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arXiv · 2609.10415

A Categorical Approach to Nilspace Theory

Noa Bihlmaier·Nick Ruoff
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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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Noa Bihlmaier, Nick Ruoff. 2026-09-09. A Categorical Approach to Nilspace Theory. https://arxiv.org/abs/2609.10415

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