Covering groupoids of categorical groups

Abstract

If $X$ is a topological group, then its fundamental groupoid ${\pi }_{1}X$ is a group-groupoid which is a group object in the category of groupoids. Further if $X$ is a path connected topological group which has a simply connected cover, then the category of covering spaces of $X$ and the category of covering groupoids of ${\pi }_{1}X$ are equivalent. In this paper we prove that if $(X,x_0)$ is an $H$-group, then the fundamental groupoid ${\pi }_{1}X$ is a categorical group. This enable us to prove that the category of the covering spaces of an $H$-group $(X,x_0)$ is equivalent to the category of covering groupoid of the categorical group ${\pi }_{1}X$.

15 pages, research article, LaTeX2e, xypic

Cited by in corpus (1)

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