Suborbifolds and groupoid embeddings

TL;DR

This paper explores the relationship between suborbifolds and groupoid embeddings, establishing criteria for when groupoid embeddings correspond to suborbifolds and identifying classes of suborbifolds that naturally induce such embeddings.

Contribution

It provides a detailed analysis of the correspondence between suborbifolds and groupoid embeddings, clarifying which embeddings arise from suborbifolds and identifying natural classes of suborbifolds.

Findings

Characterization of groupoid embeddings corresponding to suborbifolds

Identification of classes of suborbifolds leading to groupoid embeddings

Enhanced understanding of orbifold groupoid and suborbifold correspondence

Abstract

Given the notion of suborbifold of the second author (based on ideas of Borzellino/Brunsden) and the classical correspondence (up to certain equivalences) between (effective) orbifolds via atlases and effective orbifold groupoids, we analyze which groupoid embeddings correspond to suborbifolds and give classes of suborbifolds naturally leading to groupoid embeddings.