A Note on the Soft Group Category

TL;DR

This paper introduces the structure of the soft group category, identifying key objects and morphisms, and establishing it as a symmetric monoidal category, contributing to the theoretical understanding of soft algebraic structures.

Contribution

It defines the soft group category, characterizes important objects and morphisms, and proves its symmetric monoidal structure, advancing soft algebraic theory.

Findings

Soft group category has a well-defined structure.

Identifies universal objects like final object and product.

Proves the category is symmetric monoidal.

Abstract

The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the category of soft groups is a symmetric monodial category.