Categories without structures

Rodin, Andrei (2009) Categories without structures.

Abstract

The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies “invariant forms” (Awodey) categorical mathematics studies covariant transformations which, generally, don’t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.