Furthermore, all strict pseudo-limits are PIE-limits, and therefore any strict 2-category which admits all PIE-limits also admits all non-strict 2-limits, although it may not have all strict 2-limits. This is the case, for instance, for the 2-category of strict algebras and pseudo morphisms over a strict 2-monad.

PIE-limits can also be characterized as the coalgebras for a pseudo morphism classifier?comonad, exhibiting them as a 2-categorical version of the notion of rigged limit.