Covering theory for strict 2-groupoids via actions, quotients, and crossed modules over groupoids
AIMS MATHEMATICS, cilt.11, sa.8, ss.27370-27395, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 11 Sayı: 8
- Basım Tarihi: 2026
- Doi Numarası: 10.3934/math.20261095
- Dergi Adı: AIMS MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.27370-27395
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Recep Tayyip Erdoğan Üniversitesi Adresli: Evet
Özet
This paper establishes a direct correspondence between the geometric covering theory of strict 2-groupoids and the algebraic lifting theory of crossed modules over groupoids. Working entirely within an object-preserving framework, we prove a chain of categorical equivalences linking strict 2-groupoid actions, covering strict 2-groupoids, liftings of crossed modules, and covering crossed modules. Additionally, we introduce a quotient theory for strict 2-groupoids via normal 2-group bundles. We demonstrate that this quotient construction preserves the covering property and naturally induces canonical lifting crossed modules, providing a unified perspective on these geometric and algebraic structures.