On the generic solution toP(X) congruent with X in distributive categories Original Research Article

Lawvere [6] introduced the notion of an algebraic theory, and the notion of a generic object of a given algebraic type — a particular object in the classifying category for algebraic objects in categories with products. In this paper we shall examine the notion of algebraic theories extended to distributive categories, and analyse in detail a particular case, namely isomorphismsP(X) congruent with X for a polynomialP. Examples of the general problem have been studied in [2](P(X) = X2 + 1, solving a problem posed in [7]), [5](P(X) = X + 1) and [8] (P(X) = 2X + 1).