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Categories in Context: Historical, Foundational, and Philosophical

Identifieur interne : 001610 ( Istex/Curation ); précédent : 001609; suivant : 001611

Categories in Context: Historical, Foundational, and Philosophical

Auteurs : Elaine Landry [Canada] ; Jean-Pierre Marquis [Canada]

Source :

RBID : ISTEX:6C037185D05FFDCD17ECD03BE771DD3550F1BC10

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Abstract

The aim of this paper is to put into context the historical, foundational and philosophical significance of category theory. We use our historical investigation to inform the various category-theoretic foundational debates and to point to some common elements found among those who advocate adopting a foundational stance. We then use these elements to argue for the philosophical position that category theory provides a framework for an algebraic in re interpretation of mathematical structuralism. In each context, what we aim to show is that, whatever the significance of category theory, it need not rely upon any set-theoretic underpinning.

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DOI: 10.1093/philmat/nki005

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ISTEX:6C037185D05FFDCD17ECD03BE771DD3550F1BC10

Le document en format XML

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<name sortKey="Marquis, Jean Pierre" sort="Marquis, Jean Pierre" uniqKey="Marquis J" first="Jean-Pierre" last="Marquis">Jean-Pierre Marquis</name>
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<term>Abstract level</term>
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<term>Abstract structure</term>
<term>Abstract structures</term>
<term>Abstract system</term>
<term>Abstract systems</term>
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<term>Adjoint functor</term>
<term>Adjoint functors</term>
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<term>Algebraic geometry</term>
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<term>Concrete systems</term>
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<term>Continuous mappings</term>
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<term>Foundational research</term>
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<term>Fregean demand</term>
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<term>Makkai</term>
<term>Mathematica</term>
<term>Mathematical concept</term>
<term>Mathematical concepts</term>
<term>Mathematical knowledge</term>
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<term>Mathematics</term>
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<term>Morphisms</term>
<term>Natural isomorphisms</term>
<term>Natural numbers</term>
<term>Natural transformation</term>
<term>Other words</term>
<term>Oxford university press</term>
<term>Philma</term>
<term>Philosophia</term>
<term>Philosophia mathematica</term>
<term>Philosophical position</term>
<term>Possible types</term>
<term>Princeton university press</term>
<term>Pure intuitionistic type theory</term>
<term>Resnik</term>
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<term>Same type</term>
<term>Schematic type</term>
<term>Schematic types</term>
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<term>Sheaf theory</term>
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<term>Structure theory</term>
<term>Subject matter</term>
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<term>Symbolic logic</term>
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<div type="abstract" xml:lang="en">The aim of this paper is to put into context the historical, foundational and philosophical significance of category theory. We use our historical investigation to inform the various category-theoretic foundational debates and to point to some common elements found among those who advocate adopting a foundational stance. We then use these elements to argue for the philosophical position that category theory provides a framework for an algebraic in re interpretation of mathematical structuralism. In each context, what we aim to show is that, whatever the significance of category theory, it need not rely upon any set-theoretic underpinning.</div>
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