Author: fpaugam Format: TextIs the notion of local Kan extension in weak or infinity n-categories well defined. I know there is the infinity,1-case done by Lurie, but it is not local. I would define a Kan extension as the datum of a 1-morphism filling the usual diagram, with a 2-morphism that induces an equivalence of (n-2)-categories of morphisms between morphisms. You may do the same in the infinity,n case, if needed.
Is there a better definition?
The point is to define limits in weak n-categories using this. It is not simpler to define limit than to define Kan extensions.
Are there finer notions of local extensions, that use more explicitely the higher category structure?
Is the notion of local Kan extension in weak or infinity n-categories well defined. I know there is the infinity,1-case done by Lurie, but it is not local. I would define a Kan extension as the datum of a 1-morphism filling the usual diagram, with a 2-morphism that induces an equivalence of (n-2)-categories of morphisms between morphisms. You may do the same in the infinity,n case, if needed.
Is there a better definition?
The point is to define limits in weak n-categories using this. It is not simpler to define limit than to define Kan extensions.
Are there finer notions of local extensions, that use more explicitely the higher category structure?
Author: Mike Shulman Format: MarkdownItexDidn't we already [have this discussion](http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=2896&page=1)?