By a ‘completion’ on a 2-category K we mean here an idempotent pseudomonad on K . We are particularly interested in pseudomonads that arise from KZdoctrines. Motivated by a question of Lawvere, we compare the Cauchy completion [23], defined in the setting of V-Cat for V a symmetric monoidal closed category, with the Grothendieck completion [7], defined in the setting of S-Indexed Cat for S a to...