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arXiv · 2606.21952

A bicategorical perspective on Steinberg algebras

Ralf Meyer·Fabian Rodatz·Taufik Yusof
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Abstract

We show that the Steinberg algebra construction for ample groupoids is part of a pseudofunctor from the bicategory of ample groupoids and groupoid correspondences to the bicategory of rings with local units and nondegenerate bimodules. We define a covariance ring for diagrams in this bicategory of rings and show that it is a bicategorical limit. We compute the covariance ring for a diagram of ``proper'' bimodules over an Ore monoid. For diagrams coming from groupoid correspondences, we identify the covariance ring with the Steinberg algebra of its groupoid model.

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Ralf Meyer, Fabian Rodatz, Taufik Yusof. 2026-06-20. A bicategorical perspective on Steinberg algebras. https://arxiv.org/abs/2606.21952

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