So far I have that an equilibrium in dominant strategies is one where two strictly dominant strategy profiles meet (e.g. to report the other prisoner in the Prisoner's Dilemma). Going by the definition of a dominant strategy, it is one where the strategy profile is the best no matter what the opponent chooses, and hence would also fit the Nash equilibrium definition where neither player has incentive to change their strategy since by definition the dominant strategy is already the best one.
However, this seems too simple - am I missing anything?
Thanks!