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- Kan_extension abstract "Kan extensions are universal constructs in category theory, a branch of mathematics. They are closely related to adjoints, but are also related to limits and ends. They are named after Daniel M. Kan, who constructed certain (Kan) extensions using limits in 1960.An early use of (what is now known as) a Kan extension from 1956 was in homological algebra to compute derived functors.In Categories for the Working Mathematician Saunders Mac Lane titled a section \"All Concepts Are Kan Extensions\", and went on to write thatThe notion of Kan extensions subsumes all the other fundamental concepts of category theory.Kan extensions generalize the notion of extending a function defined on a subset to a function defined on the whole set. The definition, not surprisingly, is at a high level of abstraction. When specialised to posets, it becomes a relatively familiar type of question on 'constrained optimization'.".
- Kan_extension thumbnail Right_Kan_Extension.png?width=300.
- Kan_extension wikiPageID "2502518".
- Kan_extension wikiPageLength "8145".
- Kan_extension wikiPageOutDegree "36".
- Kan_extension wikiPageRevisionID "672224676".
- Kan_extension wikiPageWikiLink Adjoint_functors.
- Kan_extension wikiPageWikiLink Categories_for_the_Working_Mathematician.
- Kan_extension wikiPageWikiLink Category:Adjoint_functors.
- Kan_extension wikiPageWikiLink Category:Category_theory.
- Kan_extension wikiPageWikiLink Category_theory.
- Kan_extension wikiPageWikiLink Comma_category.
- Kan_extension wikiPageWikiLink Copower_(category_theory).
- Kan_extension wikiPageWikiLink Daniel_Kan.
- Kan_extension wikiPageWikiLink Derived_functor.
- Kan_extension wikiPageWikiLink Dual_(category_theory).
- Kan_extension wikiPageWikiLink End_(category_theory).
- Kan_extension wikiPageWikiLink Functor.
- Kan_extension wikiPageWikiLink Graduate_Texts_in_Mathematics.
- Kan_extension wikiPageWikiLink Homological_algebra.
- Kan_extension wikiPageWikiLink Limit_(category_theory).
- Kan_extension wikiPageWikiLink Mathematics.
- Kan_extension wikiPageWikiLink Natural_transformation.
- Kan_extension wikiPageWikiLink Opposite_category.
- Kan_extension wikiPageWikiLink Partially_ordered_set.
- Kan_extension wikiPageWikiLink Princeton_University_Press.
- Kan_extension wikiPageWikiLink Saunders_Mac_Lane.
- Kan_extension wikiPageWikiLink Springer_Science+Business_Media.
- Kan_extension wikiPageWikiLink Subdivided_interval_categories.
- Kan_extension wikiPageWikiLink Universal_property.
- Kan_extension wikiPageWikiLink File:Kan_extension_universal_property_diagram.png.
- Kan_extension wikiPageWikiLink File:Right_Kan_Extension.png.
- Kan_extension wikiPageWikiLink File:Right_Kan_extension_universal_property_diagram.PNG.
- Kan_extension wikiPageWikiLinkText "Kan Extension".
- Kan_extension wikiPageWikiLinkText "Kan extension of a functor".
- Kan_extension wikiPageWikiLinkText "Kan extension".
- Kan_extension wikiPageUsesTemplate Template:Cite_book.
- Kan_extension wikiPageUsesTemplate Template:Reflist.
- Kan_extension subject Category:Adjoint_functors.
- Kan_extension subject Category:Category_theory.
- Kan_extension hypernym Constructs.
- Kan_extension type Function.
- Kan_extension type Functor.
- Kan_extension type Theory.
- Kan_extension comment "Kan extensions are universal constructs in category theory, a branch of mathematics. They are closely related to adjoints, but are also related to limits and ends. They are named after Daniel M.".
- Kan_extension label "Kan extension".
- Kan_extension sameAs Q1723418.
- Kan_extension sameAs Kan-Erweiterung.
- Kan_extension sameAs Extension_de_Kan.
- Kan_extension sameAs Kan拡張.
- Kan_extension sameAs 칸_확대.
- Kan_extension sameAs m.07jc8w.
- Kan_extension sameAs Q1723418.
- Kan_extension wasDerivedFrom Kan_extension?oldid=672224676.
- Kan_extension depiction Right_Kan_Extension.png.
- Kan_extension isPrimaryTopicOf Kan_extension.
