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arXiv · 2111.10869

The bicategory of groupoid correspondences

Celso Antunes·Joanna Ko·Ralf Meyer
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Abstract

We define a bicategory with \'etale, locally compact groupoids as objects and suitable correspondences, that is, spaces with two commuting actions as arrows; the 2-arrows are injective, equivariant continuous maps. We prove that the usual recipe for composition makes this a bicategory, carefully treating also non-Hausdorff groupoids and correspondences. We extend the groupoid C*-algebra construction to a homomorphism from this bicategory to that of C*-algebra correspondences. We describe the C*-algebras of self-similar groups, higher-rank graphs, and discrete Conduch\'e fibrations in our setup.

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Celso Antunes, Joanna Ko, Ralf Meyer. 2021-11-21. The bicategory of groupoid correspondences. https://arxiv.org/abs/2111.10869

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