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Categories without structures

Rodin, Andrei (2009) Categories without structures. [Preprint]

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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 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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    Item Type: Preprint
    Keywords: structuralism, structure, category, faoundations
    Subjects: Specific Sciences > Mathematics
    Depositing User: Andrei Rodin
    Date Deposited: 30 Jul 2009
    Last Modified: 07 Oct 2010 11:18
    Item ID: 4788
    URI: http://philsci-archive.pitt.edu/id/eprint/4788

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