Topological Group-Groupoids and Equivalent Categories
Öz
The concept of groupoid was offered by Brandt (1926). The structure of the topological groupoid was given by Ehresmann (1958). A groupoid action is a significant appliance in algebraic topology offered by Ehresmann. Another algebraic notion is a covering given by Brown (1988). The topological group-groupoids (Γ-groupoid) were first put forward by Icen & Ozcan (2001). The definition of coverings of topological Γ groupoid and actions of topological Γ-groupoid were also presented by Icen et al. (2005). In this paper, we are going to create a category TΓGpdCov(Γ) of covering morphisms of TΓ-groupoid and a category TΓGpdOp(Γ) of actions of TΓ-groupoid. We will then prove that these categories are equivalent.
Anahtar Kelimeler
Teşekkür
This paper was presented in 4th International Conference on Pure and Applied Mathematics (ICPAM - VAN 2022), Van-Turkey, June 22-23, 2022.
Kaynakça
- Brandt, H. (1926). Uber ein verallgemeinerung des Gruppen begriffes. Mathematische Annalen, 96, 360-366. doi: 10.1007/BF01209171
- Brown, R., & Danesh-Naruie, G. (1975). The fundamental groupoid as a topological groupoid. Proceedings of the Edinburgh Mathematical Society, 19-2(3), 237-244. doi: 10.1017/S0013091500015509
- Brown, R., Danesh-Naruie, G., & Hardy, J. P. L. (1976). Topological groupoids II: Covering morphism and G-space. Mathematische Nachrichten, 74, 143-145. doi: 10.1002/mana.3210740110
- Brown, R., & Spencer, C. B. (1976). G-groupoids, crossed modules and the fundamental groupoid of a topological group. Proceedings of the Koninklijke Nedderlandse Akademie van Wetenschappen, 79, 196-302. doi: 10.1016/1385-7258(76)90068-8
- Brown, R. (1988). Topology: A Geometric Account of General Topology, Homotopy Types and the Fundamental Groupoid. Chichester, England: Ellis Horwood.
- Ehresmann, C. (1958). Categories topologiques et categories differentiables. Colloque de Geometrie Differentielle Globale, Cenrtre Belge de Recherches Mathematiques, Bruxelles, 137-150.
- Icen, I., & Ozcan, A. F. (2001). Topological crossed modules and G groupoids. Algebras, Groups and Geometries, 18, 401-410.
- Icen, I., Ozcan, A. F., & Gursoy, M. H. (2005). Topological group-groupoids and their coverings. Indian Journal of Pure and Applied Mathematics, 36(9), 493-502.