Covering Morphisms of Local Topological Group-Groupoids

Abstract

Let L be a local topological group whose underlying space has a universal cover. Then the fundamental groupoid $$\pi _1(L)$$ becomes a local topological group-groupoid. In this paper, we prove that the slice category $${\mathsf {LTGpCov}}/L$$ of covering moprphisms $$p:\widetilde{L}\rightarrow L$$ of local topological groups in which $$\widetilde{L}$$ has also a universal cover and the category $${\mathsf {LTGpGdCov}}/\pi _{1}(L)$$ of covering morphisms $$q:\widetilde{G}\rightarrow \pi _1(L) $$ of local topological group-groupoids based on $$\pi _1(L)$$ are equivalent.