Topological Group-Groupoids and Equivalent Categories-Reference-Cited by-同舟云学术

Topological Group-Groupoids and Equivalent Categories

Published:2022-08-25 Issue: Volume: Page:
ISSN:1300-5413
Container-title:Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi
language:tr
Short-container-title:YYUFBED

Author:

ÖZCAN Abdullah Fatih¹,İÇEN İlhan²

Affiliation:

1. İNÖNÜ ÜNİVERSİTESİ

2. INONU UNIVERSITY, FACULTY OF ARTS AND SCIENCES

Abstract

The 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 which is offered by Ehresmann. Another algebraic notion is a covering given by Brown (1988). The topological group-groupoids (Γ-groupoid) were first provided by İçen & Ozcan (2001). The definition of coverings of topological Γ groupoid and actions of topological Γ-groupoid were also given by İçen et al.(2005). In this paper, we will create a category TΓGpdCov(Γ) of coverings of topological Γ-groupoid and a category TΓGpdOp(Γ) of actions of topological Γ-groupoid. And then we will prove that these categories are equivalent.

Publisher

Van Yuzuncu Yil University

Reference8 articles.

1. Brandt, H. (1926). Uber ein verallgemeinerung des Gruppen begriffes. Math. Ann., 96, 360-366.

2. Ehresmann, C. (1958). Categories topologiques et categories differentiables. Colloque de Geometrie Differentielle Globale, Cenrtre Belge de Recherches Mathematiques, Bruxelles, 137-150.

3. Brown, R. (1988). Topology: A geometric account of general topology, homotopy types, and the fundamental groupoid. Ellis Horwood, Chichester.

4. Icen, I. & Ozcan, A.F. (2001). Topological crossed modules and G groupoids. Algebras, Groups Geom. 18, 401-410.

5. Icen, I. & Ozcan, A.F.& Gursoy, M.H. (2005). Topological Group-Groupoids and Their Coverings. Indian J. pure appl. Math., 36(9), 493-502.