An elementary approach to sofic groupoids

TL;DR

This paper introduces an elementary framework for understanding sofic groupoids, establishes key permanence properties, and demonstrates that soficity can be characterized solely by the full group, addressing a question in the field.

Contribution

It provides a simplified approach to sofic groupoids and shows that soficity can be determined from the full group alone, answering an open question.

Findings

Sofic groupoids can be described using elementary methods.

Soficity is preserved under certain operations.

Soficity can be characterized by the full group alone.

Abstract

We describe sofic groupoids in elementary terms and prove several permanence properties for sofcity. We show that sofcity can be determined in terms of the full group alone, answering a question by Conley, Kechris and Tucker-Drob.