Guild Wars 2

Question about on critical hit sigils.

If I have the same sigil on another weapon set, does the cooldown apply to both?
Or the cooldown applies to the one that triggered, and if I switch to the other weapon set, that one can trigger again with it’s own cooldown?

Lets say I have Two weapon sets, my first weapon set a have a Sigil of Generosity and if I switch to the second weapon set I have a Sigil of Generosity of that too.

If the sigil triggers on the first set, does it trigger a cooldown for the sigil on the other set too?

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