Categories without Structures

Philosophia Mathematica 19 (1):20-46 (2011)
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 form’ (Awodey) categorical mathematics studies covariant and contravariant transformations which, generally, have no invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics
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DOI 10.1093/philmat/nkq027
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References found in this work BETA
Three Varieties of Mathematical Structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.
Exploring Categorical Structuralism.C. Mclarty - 2004 - Philosophia Mathematica 12 (1):37-53.
Structure in Mathematics.Saunders Lane - 1996 - Philosophia Mathematica 4 (2):174-183.

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Invariants and Mathematical Structuralism.Georg Schiemer - 2013 - Philosophia Mathematica 22 (1):70-107.

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