Equivalence of Fell bundles is an equivalence relation

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 $\mathcal{B}$ and $\mathcal{C}$ and another equivalence between $\mathcal{C}$ and $\mathcal{D}$, we construct an equivalence between $\mathcal{B}$ and $\mathcal{D}$ out of the tensor product bundle. As a consequence, we obtain that Fell bundle equivalence is indeed an equivalence relation.

42 pages

References in corpus (1)

• Fell bundles over inverse semigroups and twisted etale groupoids

Cited by in corpus (1)

• The Imprimitivity Fell Bundle