First Isomorphism Theorem for Cat-1 groupoids
10th International Conference of Mathematical Sciences (ICMS 2026), İstanbul, Türkiye, 2 - 06 Eylül 2026, ss.18, (Özet Bildiri)
- Yayın Türü: Bildiri / Özet Bildiri
- Basıldığı Şehir: İstanbul
- Basıldığı Ülke: Türkiye
- Sayfa Sayıları: ss.18
- Recep Tayyip Erdoğan Üniversitesi Adresli: Evet
Özet
Cat-1 groupoids (or cat1 -groupoids) constitute a natural generalization of cat1 -groups and provide an algebraic framework closely related to crossed modules over groupoids. Motivated by the classical First Isomorphism Theorem for groups, we establish an analogous theorem in the category of cat1 -groupoids. For a morphism of cat1 -groupoids, we introduce the corresponding kernel cat1 -groupoid and prove that the quotient cat1 -groupoid modulo the kernel is naturally isomorphic to the image cat1 -groupoid. This result extends the classical isomorphism principle to the cat1 -groupoid setting. The theorem provides an effective tool for further constructions. As applications, we obtain natural actions of cat1 -groupoids and construct liftings of crossed modules over groupoids arising from quotient structures. These applications demonstrate that the First Isomorphism Theorem is not only a structural result but also a fundamental tool connecting quotient constructions, actions and lifting theories. The results contribute to the development of the algebraic theory of cat1 -groupoids and strengthen their relationship with crossed modules over groupoids.