After a brief survey of literature on the application of the category theory in computer science, new results of employing the category-theoretical constructions worked out by the authors to formalize problems of artificial intelligence are presented. The range of areas that can be described with the use of the developed category-theoretical approach is enlarged. A number of results that do not depend on the application domain are obtained. In particular, the category of substitutions and the fuzzy category are constructed and studied.
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