can you use duty or other redirections or destruction negations after a duel?
duty after a duel
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Aside: there is no "redirection" in Celestial edition.
Your question is too vague to answer it precisely, it depends on which card the duel comes from, what its consequences will be and which card you want to use against them. If you are asking whether a duel from a card is a card effect or a rulebook effect, it is a card effect, per Sources of effects: "EXCEPTION 4: Duels come from the effect that created their associated challenge, not the rulebook."
For instance Duty will negate the destruction from another player's card's effect (action or trait) while Strength of the Bamboo will do so only if the duel comes from an action that targets your Hero Personality. As a consequence if one of your Hero Personalities lobbies (for example), the destruction from Enough Talk! will be negated by Duty but not by Strength of the Bamboo because Enough Talk! does not target the performing Hero.