Categories without Structures

Philosophia Mathematica 19 (1):20-46 (2011)
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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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10.1093/philmat/nkq027

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Andrei Rodin
Russian Academy of Sciences

Citations of this work

Invariants and Mathematical Structuralism.Georg Schiemer - 2014 - Philosophia Mathematica 22 (1):70-107.
Does Identity Make Sense?Andrei Rodin - 2024 - Manuscrito 47 (1):2024-0073.

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References found in this work

Background.[author unknown] - 2004 - The Chesterton Review 30 (3-4):411-413.
Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
Structure in mathematics and logic: A categorical perspective.S. Awodey - 1996 - Philosophia Mathematica 4 (3):209-237.

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