There seem to be two definitions of what a saturated class should be:

1. A class of morphisms closed under retracts, pushouts and transfinite composition.
2. A class of monomorphisms containing all isomomorphisms, closed under retracts, pushouts, arbitrary coproducts and countable composition.

My question is, does it make a difference which definition one choses in the context of the cofibrantly generated modelstructures on

• $\mathbf{Top}$, with respect to the Quillen model structure
• $\mathbf{sSet}$, with respect to the Quillen (or Kan) Model structure
• $\mathbf{Cat}$, with respect to the Thomason model structure

(I'm perfectly happy with partial answers, so if someone's got an answer for at least one of the listed categories, feel free to post it)