About covering spaces, covering and action groupoids
8th International Conference of Mathematical Sciences, ICMS 2024, Hybrid, Istanbul, Turkey, 11 - 15 September 2024, vol.3431, (Full Text)
- Publication Type: Conference Paper / Full Text
- Volume: 3431
- Doi Number: 10.1063/5.0290308
- City: Hybrid, Istanbul
- Country: Turkey
- Keywords: action groupoid, covering groupoid, Covering space
- Erciyes University Affiliated: Yes
Abstract
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.