Let $\mathcal{M}$ be a

locally finitely presentable model category, cofibrantly generated by two sets $\mathcal{I}$ and $\mathcal{J}$ of cofibrations and trivial cofibrations with presentable domain and codomain.

I know that weak equivalences and fibrations are stable by filtered colimits.

What can be said about cofibrations and trivial cofibrations?

Is there a class of good examples in which this is known to be true?

Are there additional axioms that can be imposed that ensure this?

finitelypresentable domain and codomain? $\endgroup$