Categories as formal models of calculations

Abstract

Various formal models of calculations are considered. In particular, recursive functions, fuzzy models and categorical models. It is shown how functions are calculated based on such models. In each of these models, the concept of number and basic arithmetic operations are introduced. It is concluded that the considered formal models of calculations can be represented within certain categories and an abstract theory of computability and relevant programming languages can be built on a categorical basis. That is, we are talking about the creation of a universal programming language in which it would be possible to describe problems from various subject areas by interpreting them in the appropriate categories with the futher use of a universal categorical apparatus for their solution. Such a language should be oriented to scientific problems.