Category Theory Applied in Different Uniform Spaces

This book explores the fascinating world of category theory and its application in various branches of mathematics, offering a unified framework for understanding uniform structures. From its origins in the work of Eilenberg and MacLane, category theory has become a powerful tool for abstractly expressing mathematical concepts. The book covers fundamental topics such as categories, functors, and morphisms, with a special focus on fuzzy set theory and the development of uniform structures in fuzzy topological spaces. By introducing the concept of a uniform environment, the book presents a novel approach for unifying classical, probabilistic, and Hutton uniform environments, shedding new light on transformations across different mathematical structures. The interdisciplinary relevance of this theory is also highlighted through its application to symmetry analysis in molecules.