  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.
