COVERING GROUPOIDS OF CATEGORICAL GROUPS

Authors : O. MUCUK, T. ŞAHAN

Pages : 419-430

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Publication Date : 2013-04-01

Article Type : Research Paper

Abstract :If X is a topological group, then its fundamental groupoid π1insert ignore into journalissuearticles values(X); is agroup-groupoid which is a group object in the category of groupoids.Further if X is a path connected topological group which has a simplyconnected cover, then the category of covering groups of X and thecategory of covering groupoids of π1insert ignore into journalissuearticles values(X); are equivalent. In this paperwe prove that if insert ignore into journalissuearticles values(X, x0); is an H-group, then the fundamental groupoidπ1insert ignore into journalissuearticles values(X); is a weak categorical group. This enables one to prove that thecategory of the covering spaces of an H-group insert ignore into journalissuearticles values(X, x0); is equivalent tothe category of covering groupoids of the weak categorical group π1insert ignore into journalissuearticles values(X);
Keywords : H group, covering groupoid and categorical group