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arXiv · 2203.12068

Groupoid models for diagrams of groupoid correspondences

Ralf Meyer
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Abstract

A diagram of groupoid correspondences is a homomorphism to the bicategory of \'etale groupoid correspondences. We study examples of such diagrams, including complexes of groups and self-similar higher-rank graphs. We encode the diagram in a single groupoid, which we call its groupoid model. The groupoid model is defined so that there is a natural bijection between its actions on a space and suitably defined actions of the diagram. We describe the groupoid model in several cases, including a complex of groups or a self-similar group. We show that the groupoid model is a bilimit in the bicategory of groupoid correspondences.

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Ralf Meyer. 2022-03-22. Groupoid models for diagrams of groupoid correspondences. https://arxiv.org/abs/2203.12068

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