Abstract In many algebraic settings, the categories of crossed modules, cat 1 cat^{1} -objects, and internal categories are known to be categorically equivalent. In this paper, we develop this correspondence in the category in self-acting groups. We first construct crossed modules, cat 1 cat^{1} -objects, and internal categories in this context and establish their fundamental structural properties. We then prove that the categories of these three types of objects in the category of self-acting groups are equivalent. This provides a unified categorical framework for interpreting higher-dimensional algebraic structures arising from self-actions.
Ali AYTEKİN (Thu,) studied this question.