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@Velocio
TBH I find it easier to think of the climb category WRT to the myth that it's the gear you need in a Citroen 2CV to get over it:
http://inrng.com/2015/07/tour-climbs-category-formula/
(in the comments http://inrng.com/2015/07/tour-climbs-category-formula/#comment-132636 )
Cat 4 = 4th gear
Cat 3 = 3rd gear
Cat 2 = 2nd gear
Cat 1 = 1st gear
HC = Your Citroen 2CV is not getting over this mountain
That may be just myth, but I find it easier to think about the difficulty of a climb with that cute little car in mind.