On n-tuple principal bundles

TL;DR

This paper introduces the concept of n-tuple principal bundles, extending the idea of principal bundles through compatibility conditions involving Lie group actions on groupoids.

Contribution

It develops the theoretical framework for double and n-tuple principal bundles based on compatibility conditions for Lie group actions on groupoids.

Findings

Defines the structure of n-tuple principal bundles.

Establishes compatibility conditions for Lie group actions.

Provides a foundation for further geometric and algebraic studies.

Abstract

We develop the concept of a double (more generally n-tuple) principal bundle departing from a compatibility condition for a principal action of a Lie group on a groupoid.