Categorical approach to rigidity of Roe-like algebras of coarse spaces

Kostyantyn Krutoy

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arXiv · 2503.07398

Categorical approach to rigidity of Roe-like algebras of coarse spaces

Kostyantyn Krutoy

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Abstract

We demonstrate that any full and faithful $*$-functor between approximable categories of locally finite coarse spaces induces a coarse embedding between the underlying spaces. Furthermore, we establish a general characterisation of such $*$-functors between approximable categories and prove that the functor associating each locally finite coarse space with its approximable category is full and faithful.

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Kostyantyn Krutoy. 2025-03-10. Categorical approach to rigidity of Roe-like algebras of coarse spaces. https://arxiv.org/abs/2503.07398

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