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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 mathematicsAuthor's Profile
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Citations of this work
Invariants and Mathematical Structuralism.Georg Schiemer - 2014 - Philosophia Mathematica 22 (1):70-107.
The Mathematical Description of a Generic Physical System.Federico Zalamea - 2015 - Topoi 34 (2):339-348.
Chasing Individuation: Mathematical Description of Physical Systems.Zalamea Federico - 2016 - Dissertation, Paris Diderot University
References found in this work
Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl.Gottlob Frege - 1884 - Wittgenstein-Studien 3 (2):993-999.
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.
An answer to Hellman's question: ‘Does category theory provide a framework for mathematical structuralism?’.Steve Awodey - 2004 - Philosophia Mathematica 12 (1):54-64.
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