BourbakiV1, France, Analysis, bibRecord, 000270

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

Identifieur interne : 000270 ( France/Analysis ); précédent : 000269; suivant : 000271

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

Auteurs : Ralf Krömer [France]

Source :

RBID : Hal:tel-00151000

Descripteurs français

mix :
- Eilenberg, Grothendieck, Mac Lane, Peirce, Poincaré, Wittgenstein, algèbre homologique, fondements des mathématiques, géométrie algébrique, objet, outil, pragmatisme, théorie des catégories, théorie des ensembles, topologie algébrique.

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 Unpublished sources show that Grothendieck quit the Bourbaki group because of a debate on CT, which was partly epistemological in nature, especially as far as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).

Url:

https://tel.archives-ouvertes.fr/tel-00151000

Affiliations:

Links toward previous steps (curation, corpus...)

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to stream France, to step Extraction: 000270

Links to Exploration step

Hal:tel-00151000

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A historical and philosophical tribute.</title>
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Un hommage historio-philosophique</title>
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A historical and philosophical tribute.</title>
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Un hommage historio-philosophique</title>
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A historical and philosophical tribute.
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Category theory: its mathematical achievements, its epistemological implications.A historical and philosophical tribute.

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

Source :

Descripteurs français

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri

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

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