Consult this paper by Andrei Rodin for an interpretation of category theory without structures. His central claim (from the abstract) is that while structuralism in the philosophy of mathematics studies "invariant form" (for instance, the sentences of a categorical theory are ...
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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.