On slim double Lie groupoids

TL;DR

This paper demonstrates that slim double Lie groupoids with proper core actions can be fully characterized by a specific factorization of an associated diagonal Lie groupoid, providing a new structural insight.

Contribution

It introduces a novel characterization of slim double Lie groupoids via factorization of a canonical diagonal Lie groupoid, advancing the understanding of their structure.

Findings

Slim double Lie groupoids with proper core actions are determined by a diagonal Lie groupoid factorization.

Provides a new method to classify slim double Lie groupoids.

Establishes a canonical correspondence between these groupoids and their diagonal factorizations.

Abstract

We prove that every slim double Lie groupoid with proper core action is completely determined by a factorization of a certain canonically defined "diagonal" Lie groupoid.