About covering spaces, covering and action groupoids

MUCUK O., Yüzak A.

8th International Conference of Mathematical Sciences, ICMS 2024, Hybrid, Istanbul, Türkiye, 11 - 15 Eylül 2024, cilt.3431, (Tam Metin Bildiri) identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 3431
  • Doi Numarası: 10.1063/5.0290308
  • Basıldığı Şehir: Hybrid, Istanbul
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: action groupoid, covering groupoid, Covering space
  • Erciyes Üniversitesi Adresli: Evet

Özet

For a topological space X with a universal cover, there is an equivalence between the covering spaces of X and covering morphisms of the fundamental groupoid of X. Momeover actions of a groupoid G on sets and the covering morphisms of G are categorically equivalent. In this work we consider these types of equivalences in the product setting together with some counter examples. We will indicate with some counterexamples that these do not quite work for product case and therefore we made same restrictions on the objects to get the equivalences.