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- W3088506142 abstract "The natural transformation constitutes one of the most important entity of category theory and it introduces a piece of sophisticated dynamism to the categorial structures. Each natural transformation forms a unique mapping between the so-called functors, which live between categories. In the most simple contexts, natural transformations may be recognized by commutativity of diagrams, which determine them. In fact, the natural transformation does not form any single mapping, but a pair of two components, which–together with the commutativity condition itself–introduces a kind of a symmetry to the functor diagrams. Meanwhile, the general form of the natural transformation may be predicted by means the so-called Yoneda’s lemma in each scenario based on two-valued logic. Meanwhile, the situation may be radically different if we deal with multi-diagrams (instead of the single ones) and if we exchange the two-valued scenario for a multi-valued or fuzzy one. Due to this background–the paper introduces a new concept of multi-fuzzy natural transformation. Its definition exploits the notion of fuzzy natural transformation. Moreover, a multi-fuzzy Yoneda’s lemma is formulated and proved. Finally, some references of these constructions to coding theory are elucidated in last parts of the paper." @default.
- W3088506142 created "2020-10-01" @default.
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- W3088506142 date "2020-09-22" @default.
- W3088506142 modified "2023-10-01" @default.
- W3088506142 title "The Fuzzified Natural Transformation between Categorial Functors and Its Selected Categorial Aspects" @default.
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- W3088506142 doi "https://doi.org/10.3390/sym12091578" @default.
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