TL;DR
This paper argues that category theory does not support Mathematical Structuralism and proposes a non-structuralist interpretation of categorical mathematics, impacting views on the philosophy, history, and education of mathematics.
Contribution
It introduces a non-structuralist perspective on categorical mathematics, challenging the traditional structuralist view and exploring its implications for mathematical philosophy and education.
Findings
Category theory does not inherently support Structuralism.
Categorical mathematics focuses on covariant transformations without invariants.
Implications for history and education of mathematics are discussed.
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.
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Taxonomy
TopicsHistory and Theory of Mathematics · Mathematics and Applications · Mathematical and Theoretical Analysis