Dedekind's abstract concepts: Models and mappings

Abstract

Dedekind's mathematical work is integral to the transformation of mathematics in the nineteenth century and crucial for the emergence of structuralist mathematics in the twentieth century. We investigate the essential components of what Emmy Noether called, his 'axiomatic standpoint': abstract concepts (for systems of mathematical objects), models (systems satisfying such concepts), and mappings (connecting models in a structure-preserving way).