Full Idea
An axiomatization is 'categorical' if all its models are isomorphic to one another; ..hence it has 'essentially only one' interpretation [Veblen 1904].
Gist of Idea
An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.12