A double groupoid is a type of higher groupoid structure in which there are two distinct groupoid products on the same set of arrows and must satisfy a certain compatibility law. A particular example we will focus on is that of an irrational torus, and more generally, strict 2-groups. Since groupoid structures give rise to convolution algebras, a double groupoid gives rise to two convolution products. We ask, in what sense are the two convolution products compatible?
This is based on joint work with Joel Villatoro.
Convolution Algebras of Double Groupoids and Strict 2-Groups
Convolution Algebras of Double Groupoids and Strict 2-Groups