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.

> 1) What can be said about cofibrations and trivial cofibrations? 
> 
> 2) Is there a class of good examples in which this is known to be
> true? 
> 
> 3) Are there additional axioms that can be imposed that ensure this?