A Homotopy Category Approach to Funtorial Properties of Soft Fundamental Groups

In this paper, we introduce the homotopy category [Formula: see text] by identifying soft continuous mappings that are related by soft homotopy. We consider the soft fundamental group as a functor on the category [Formula: see text] of pointed soft topological spaces and show that it assigns the same group homomorphism to homotopic soft continuous mappings. Consequently, the soft fundamental group functor naturally factors through the homotopy category, yielding a well-defined functor from [Formula: see text] to the category of groups. This establishes a homotopy-invariant categorical framework for soft topology and provides a natural categorical setting for studying the functorial properties of soft fundamental groups.