# The Equivariant Fundamental Groupoid as an Orbifold Invariant

## TL;DR

This paper develops a 2-category version of the equivariant fundamental groupoid for orbifolds and proves its Morita invariance, establishing it as a new orbifold invariant.

## Contribution

It introduces a 2-category framework for the equivariant fundamental groupoid and demonstrates its Morita invariance for representable orbifolds, advancing orbifold topology.

## Key findings

- The 2-category version generalizes the classical fundamental groupoid.
- The discrete fundamental groupoid is shown to be Morita invariant.
- This invariance makes it a robust orbifold invariant.

## Abstract

We construct a 2-category version of tom Dieck's equivariant fundamental groupoid for representable orbifolds and show that the discrete fundamental groupoid is Morita invariant; hence an orbifold invariant for representable orbifolds.