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- Q1723418 subject Q7451918.
- Q1723418 subject Q8221474.
- Q1723418 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'.".
- Q1723418 thumbnail Right_Kan_Extension.png?width=300.
- Q1723418 wikiPageWikiLink Q1322614.
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- Q1723418 wikiPageWikiLink Q579978.
- Q1723418 wikiPageWikiLink Q7098616.
- Q1723418 wikiPageWikiLink Q7451918.
- Q1723418 wikiPageWikiLink Q7631011.
- Q1723418 wikiPageWikiLink Q8221474.
- Q1723418 wikiPageWikiLink Q864475.
- Q1723418 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.".
- Q1723418 label "Kan extension".
- Q1723418 depiction Right_Kan_Extension.png.