Covering morphisms of internal groupoids in the models of a semi-abelian theory

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In this paper, for given an algebraic theory T whose category C of models is semi-abelian, we consider the topological models of T called topological T-algebras and obtain some results related to the fundamental groups of topological T-algebras. We also deal with the internal groupoid structure in the category of models providing that the fundamental groupoid deduces a functor from topological T-algebras to the internal groupoids in C and prove a criterion for the lifting of such an internal groupoid structure to the covering groupoids.