Categories Without Structures

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2 Scopus citations


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.
Original languageEnglish
Pages (from-to)20-46
JournalPhilosophia Mathematica
Issue number1
StatePublished - 2011


  • Category theory
  • Structuralism
  • Invariance
  • Functoriality


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