Covering morphisms of soft groupoids

Soft set theory has been developed as an effective mathematical tool for handling uncertainty through parameterization, leading to more practical solutions to complex problems. In parallel, the theory of covering spaces and their algebraic interpretation via groupoids has played a fundamental role in algebraic topology. Previous studies have established important categorical equivalences between coverings of spaces, coverings of groupoids, and groupoid actions on a set. In this paper, these ideas are extended to the framework of soft set theory. We introduce the notion of soft covering groupoids and define the category $SGdCov(H)$ of soft coverings of a soft groupoid $H$. Additionally, we define the actions of soft groupoids and the category $SGdOp(H)$ of soft actions of soft groupoid $H$. The main result of this study is the proof of a categorical equivalence between these two categories, thereby providing a new algebraic perspective on soft covering structures and contributing to the interaction between soft set theory and categorical topology.