Word.ws English Dictionary

Kan extension

Kan extension noun: a construct that generalizes the notion of extending a function's domain of definition.

Noun

Kan extension (plural Kan extensions)

  1. A construct that generalizes the notion of extending a function's domain of definition.
    • Moreover, f∗ admits both a left adjoint f_! and a right adjoint f_∗, given by left and right Kan extension along the map SingY→SingX, respectively. Note that this is left and right Kan extension in the ∞-categorical sense, which amounts to homotopy left and right Kan extension on the level of...2010, Matthew Ando, Andrew J. Blumberg, David Gepner, Twists of K-Theory and TMF, Robert S. Doran, Greg Friedman, Jonathan Rosenberg, Superstrings, Geometry, Topology, and C*-algebras, American...
    • We can specialise Kan extensions to the preorder setting, if we equip a preorder with a monoidal structure: an associative operation that is monotone and that has a neutral element.2012, Rolf Hinze, Kan Extensions for Program Optimisation, Or: Art and Dan Explain an Old Trick, Jeremy Gibbons, Pablo Nogueira (editors), Mathematics of Program Construction: 11th International...

Forms of Kan extension

pluralKan extensions

Origin of Kan extension

Named after Jewish and Dutch mathematician Daniel M. Kan (1927–2013), who constructed certain (Kan) extensions using limits in 1960.

Questions about Kan extension

What does Kan extension mean?
Kan extension means a construct that generalizes the notion of extending a function's domain of definition.
What part of speech is Kan extension?
Kan extension is a noun.
What is the plural of Kan extension?
The plural of Kan extension is Kan extensions.

Words near Kan extension in the dictionary

  1. kamānchas
  2. kamānche
  3. kamānches
  4. kan
  5. kan cheong
  6. Kan extension
  7. Kan extensions
  8. kan ni na
  9. kan ni na beh
  10. kan ni na beh chao chee bye
  11. kan ni na bu

Source and license

Adapted from Wiktionary: Kan extension (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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