Stephen Schanuel - Objective number theory

Classical number theory may be thought of as the arithmetic of addition, multiplication, and exponentiation of isomorphism classes of finite sets, i.e. natural numbers. Joint work with F. W. Lawvere, generalizing this to the corresponding operations on objects in more general categories, includes analogs of classical algebraic and transcendental number theory, including some results whose analogs in the classical case remain only conjectures.