# Categorical Accommodation of Graded Fuzzy Topological System, Graded Frame and Fuzzy Topological Space with Graded inclusion

## TL;DR

This paper provides a categorical analysis of graded fuzzy topological structures, including graded frames, fuzzy topological systems, and spaces with graded inclusion, building on earlier logical foundations.

## Contribution

It offers a detailed categorical framework for graded fuzzy topological concepts and explores their interrelations, extending prior logical and structural work.

## Key findings

- Established categorical relationships among graded structures
- Developed a unified framework for graded fuzzy topologies
- Extended previous logical foundations to categorical context

## Abstract

A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological system and fuzzy topological space with graded inclusion were obtained via fuzzy geometric logic with graded con- sequence. As an off shoot the notion of graded frame has been developed. This paper deals with a detailed categorical study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion and their interrelation.