Algebras, polynomials and programs

This paper presents an introduction to some of the more algebraic applications of elementary category theory in computer science. Topics include: a category based look at universal algebra; the definition of polynomials over arbitrary algebras and their application to the study of substitution; a development of Lawvere algebraic theories based on polynomials, and the application of such theories to algebra and to the study of iteration and recursion in programming languages. © 1990.