Category Algebra and Algebraic Theories

Abstract

A variety of algebras is specified by a collection of symbols of ground operations and a collection of identities. Similarly, one may speak of syntactic specification of other algebraic theories. In this chapter we point out another approach to description of algebraic theories, grounded on categorial ideas. What plays the role of the corresponding syntax is a certain category T, called an algebraic theory. Algebras of this theory are treated as functors from T into the category of sets.