In this paper we prove that the set of homotopy classes of paths in topological semigroup is a semigroup-groupoid. Further, we define the category TSGCov/X of topological semigroup coverings of X and prove that its equivalent to the category SGpGpdCov/ of covering groupoids of the semigroup-groupoid . We also prove that the topological semigroup structure of a topological semigroup-groupoid lifts to a universal topological covering groupoid.
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