Let $\frak g$ a simple finite-dimensional complex Lie algebra.

What categories of modules has the Weyl modules for $\frak g$ (in characteristic zero or positive) as projective objects?

It is an ample question, since we can see them in the category of finite-dimensional modules, in the category of finite-dimensional modules with bounded weights and so on.

Is there any reference for this stuff?

Let $\frak g$ a simple finite-dimensional complex Lie algebra.

Which categories of modules has the Weyl modules for $\frak g$ (in characteristic zero or positive) as projective objects?

It is an ample question, since we can see them in the category of finite-dimensional modules, in the category of finite-dimensional modules with bounded weights and so on.

Is there any reference for this stuff?