Kan extension

English Etymology Named after Jewish and Dutch mathematician Daniel Kan Daniel M. Kan (1927–2013), who constructed certain (Kan) extensions using limits in 1960. Noun en category theory A construct that generalizes the notion of extending a function's domain of definition. 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 Mathematical Society, page 34, Moreover, admits both a left adjoint and a right adjoint , given by left and right Kan extension along the map , 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 simplicial categories or model categories. 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. en 2013 Franz Vogler Derived Manifolds from Functors of Points Logos Verlag https://books.google.com.au/books?id=MVrTAQAAQBAJ&pg=PA5&dq=%22Kan+extension%22%7C%22Kan+extensions%22&hl=en&sa=X&ved=0ahUKEwjD7bDdi9PaAhWhgVQKHZBdBfsQ6AEI1AEwIA#v=onepage&q=%22Kan%20extension%22%7C%22Kan%20extensions%22&f=false 5 We are going to introduce the direct and inverse image functor for presheaves as special Kan extensions and show that they behave well with respect to global and local model structures on simplicial model categories. Translations construct that generalizes the extending of a function's domain of definition French: fr extension de Kan f en eponyms