| dbo:abstract |
In mathematics, derivators are a proposed frameworkpg 190-195 for homological algebra giving a foundation for both abelian and non-abelian homological algebra and various generalizations of it. They were introduced to address the deficiencies of derived categories (such as the non-functoriality of the cone construction) and provide at the same time a language for homotopical algebra. Derivators were first introduced by Alexander Grothendieck in his long unpublished 1983 manuscript Pursuing Stacks. They were then further developed by him in the huge unpublished 1991 manuscript Les Dérivateurs of almost 2000 pages. Essentially the same concept was introduced (apparently independently) by Alex Heller. The manuscript has been edited for on-line publication by Georges Maltsiniotis. The theory has been further developed by several other people, including Heller, Franke, Keller and Groth. (en) Un dérivateur est une notion mathématique introduite par Alexander Grothendieck pour essayer de rendre compte de manière catégorique des différentes théories de l'homologie et de l'homotopie, notamment en comblant les défauts des catégories dérivées. Les dérivateurs peuvent se concevoir comme un aperçu des catégories d'ordre supérieur, tout en demeurant un objet de la théorie des catégories ordinaires. (fr) |
| dbo:wikiPageExternalLink |
https://webusers.imj-prg.fr/~georges.maltsiniotis/groth/Derivateursengl.html https://ncatlab.org/nlab/show/derivator https://stacks.math.columbia.edu/tag/08LT https://golem.ph.utexas.edu/category/2018/03/stabilization_of_derivators.html |
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dbr:Algebraic_space dbr:Homotopy_colimit dbr:Derived_category dbr:Mathematics dbr:Pursuing_Stacks dbr:Triangulated_category dbr:Localization_of_a_category dbr:NLab dbr:Alexander_Grothendieck dbc:Homological_algebra dbr:Jens_Franke dbc:Homotopical_algebra dbr:Homological_algebra dbr:Homotopical_algebra dbr:Topos dbr:Scheme_(mathematics) dbr:Zariski_topology dbr:Filtered_colimit dbr:Grothendieck_site dbr:Etale_site |
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dbc:Homological_algebra dbc:Homotopical_algebra |
| gold:hypernym |
dbr:Framework |
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dbo:Software |
| rdfs:comment |
Un dérivateur est une notion mathématique introduite par Alexander Grothendieck pour essayer de rendre compte de manière catégorique des différentes théories de l'homologie et de l'homotopie, notamment en comblant les défauts des catégories dérivées. Les dérivateurs peuvent se concevoir comme un aperçu des catégories d'ordre supérieur, tout en demeurant un objet de la théorie des catégories ordinaires. (fr) In mathematics, derivators are a proposed frameworkpg 190-195 for homological algebra giving a foundation for both abelian and non-abelian homological algebra and various generalizations of it. They were introduced to address the deficiencies of derived categories (such as the non-functoriality of the cone construction) and provide at the same time a language for homotopical algebra. The manuscript has been edited for on-line publication by Georges Maltsiniotis. The theory has been further developed by several other people, including Heller, Franke, Keller and Groth. (en) |
| rdfs:label |
Derivator (en) Dérivateur (fr) |
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freebase:Derivator wikidata:Derivator dbpedia-fr:Derivator https://global.dbpedia.org/id/4j2WU |
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wikipedia-en:Derivator?oldid=1118353482&ns=0 |
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dbr:Les_Dérivateurs |
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