# What does "Kan" mean in "Kan operations"?

I'm studying Cubical Type Theory and I see the word "Kan operations" (ref1, ref2, ref3, and there are many more), which is related to "adding a cap to a tube" (can be also explained as "given a path between a and b, and two paths that are between a and c/b and d respectively, we can use Kan operations to get a path between c and d").

I wonder if there's any references that can explain where this "Kan" word come from -- what does it mean? Is that "Kan extensions" in Category theory?

• It’s a personal name. Daniel Kan. May 14 '19 at 22:29

## 1 Answer

Kan operations are likely named after Daniel M. Kan, in analogy to concepts such as Kan extensions, Kan complexes, Kan fibrations, Kan condition, and many more. Kan also introduced adjoint functors.

• Does that mean "filling something" then? May 16 '19 at 0:44
• Kan operation seems to be shorthand for Kan filling operation, but I don’t really know anything about this area. May 16 '19 at 5:19