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Category theory: its mathematical achievements, its epistemological implications.
A historical and philosophical tribute.

Abstract : Category theory (CT) is important in virtue of its mathematical applications and its power to generate philosophical debate. It is a language for algebraic topology, a deductive system in homological algebra, and, as an alternative to set theory, a means of object construction (in Grothendieck's conception of algebraic geometry). Unpublished sources show that Grothendieck quit the Bourbaki group because of a debate on CT, which was partly epistemological in nature, especially as far as set-theoretical realisation of categorical constructions was concerned. We claim that CT is fundamental because it is a theory of some typical operations of structural mathematics: in our pragmatic perspective, justification of mathematical knowledge is not provided for by the reduction to basic objects but rather by a technical common sense intervening on each level (the theories on the higher level having as their objects the theories of the original objects).
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Contributor : Ralf Krömer <>
Submitted on : Friday, June 1, 2007 - 12:22:38 PM
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  • HAL Id : tel-00151000, version 1

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Ralf Krömer. Category theory: its mathematical achievements, its epistemological implications.
A historical and philosophical tribute.. Philosophy. Université Nancy II; Universität des Saarlandes Saarbrücken, 2004. German. ⟨tel-00151000⟩

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