Touch up on 6k, 5k, etc... i see this alot... but I got to thinking that what does it really do?
Does it form a new edge? How can you "touch up" an edge that has lost its sharpness? or given that it's not that blunt, what does "touch up" really do?
Also if you touch up on a loaded strop, how can it bring it back if all it does is refine the edge?
Or does it also align the edge like you would when you use a hone?
if your edge is still functional and working well, but not quite at 100%, touching up on high grit stone works well. However, if your edge is fatigued steel, it wont work well at all. Also, you can only touch up so many times before you will need to resharpen anyways, unless your touchup stone is not too high grit and is a fast cutter... then you'd be removing enough steel to be ok.
When touching up, the idea is to sharpen in the same way and at the same angle as you normally sharpen... just on your finishing stone only.
Touching up on a strop generally ends up being sharpening at a higher angle, so it "refreshes" the edge that way.