  A. Avil\'es and C. Brech proved a intriguing result about the existence and
uniqueness of certain injective Boolean algebras or Banach spaces. Their result
refines the standard existence and uniqueness of saturated models. They express
a wish to obtain a unified approach in the context of category theory. We
provide this in the framework of weak factorization systems. Our basic tool is
the fat small object argument.
