Kan extension

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

Noun

 * 1)  A construct that generalizes the notion of extending a function's domain of definition.
 * 2) * 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,, page 34,
 * Moreover, $$f^\text{∗}$$ admits both a left adjoint $$f_\text{!}$$ and a right adjoint $$f_\text{∗}$$, given by left and right Kan extension along the map $$\text{Sing}\ Y^{\circ p}\rightarrow\text{Sing}\ X^{\circ p}$$, respectively. Note that this is left and right Kan extension in the $$\infty$$-categorical sense, which amounts to homotopy left and right Kan extension on the level of simplicial categories or model categories.
 * 1) * 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 Conference, MPC 2012, Proceedings, Springer, Lecture Notes in Computer Science: 7342, page 336,
 * 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.

Translations

 * French: extension de Kan