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arXiv · 2110.06343

Equivalence of Fell bundles is an equivalence relation

Anna Duwenig·Boyu Li
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Abstract

We introduce the notion of groupoid pre-equivalences and prove that they give rise to groupoid equivalences by taking certain quotients. Then, given an equivalence of Fell bundles $\mathscr{B}$ and $\mathscr{C}$ and another equivalence between $\mathscr{C}$ and $\mathscr{D}$, we construct an equivalence between $\mathscr{B}$ and $\mathscr{D}$ out of the tensor product bundle. As a consequence, we obtain that Fell bundle equivalence is indeed an equivalence relation.

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Anna Duwenig, Boyu Li. 2021-10-12. Equivalence of Fell bundles is an equivalence relation. https://arxiv.org/abs/2110.06343

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