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Theses

La théorie des catégories : ses apports mathématiques et ses implications épistémologiques : un hommage historico-philosophique

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 Unpublished sources show that Grothendieck quit the Bourbaki group because of a debate on CT, which was partly epistemological in nature, especially as far as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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Theses
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http://docnum.univ-lorraine.fr/prive/BUL_T_2004_0004_KROMER.pdf
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https://hal.univ-lorraine.fr/tel-01750885
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Submitted on : Thursday, March 29, 2018 - 12:57:16 PM
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  • HAL Id : tel-01750885, version 1

Citation

Ralf Krömer. La théorie des catégories : ses apports mathématiques et ses implications épistémologiques : un hommage historico-philosophique. Mathématiques générales [math.GM]. Université Nancy 2, 2004. Français. ⟨NNT : 2004NAN21004⟩. ⟨tel-01750885⟩

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