The bicategory of groupoid correspondences Article Swipe

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Homomorphism Injective function Hausdorff space Equivariant map Mathematics Rank (graph theory) Pure mathematics Algebra over a field Combinatorics

Celso Antunes , Joanna Ko , Ralf Meyer ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2111.10869 · OA: W3217790347

We define a bicategory with étale, 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 Conduché fibrations in our setup.