On Codechef, I see difficulty ranging from cakewalk, simple, easy, easy-medium, medium, medium-hard, and hard on the editorials. Can anyone provide me a loose mapping of the these difficulties on Codeforces rating?

Providing some form of data such as the rating of the problems you practice on here, compared to the difficulty you practice on Codechef would be helpful as well.

Find people who use both Codechef and Codeforces, check their time to solve problems of each difficulty, and let us know what's the mapping.

you really are a badass

I am not sure that is a right way to compare because lots of the time Codechef problem are more heavy on implementation and take more time. A better way could be that people could tell me what rated problems they solve for practice on Codeforces, and what difficulty problems they solve for practice on Codechef.