Categories without structures

Publication Year:
2009
Usage 460
Downloads 460
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Repository URL:
http://philsci-archive.pitt.edu/id/eprint/4788
Author(s):
Rodin, Andrei
preprint description
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.