The Natural Transformations with the Multi-Fuzzy Commutativity Condition

Abstract

The natural transformation – as a pilar of a functional dynamism in category theory – forms a unique transfor-mation between the so-called functors, which operate between categories and their morphisms. The natural transformations are determined by the appropriate commutativity conditions in diagrams, which co-define them and their general form may be predicted by the so-called Yoneda’s lemma. The situation seems to change radically if we exchange single diagrams for multi-diagrams. This paper is aimed at proposing a new concept of multi-fuzzy natural transformation as based on the concept of fuzzy natural transformation, which may be just defined by the scenario with multi-diagrams. It seems to be noteworthy that such a multi-fuzzy natural transformation may be referred to coding theory. In addition, a multi-fuzzy version of Yoneda’s lemma is formulated and proved.