Projective and injective objects in the category of quantales

AbstractRegular projective quantales are characterized as the weakly ∗-stable completely distributive lattices. For the class E of all onto quantale homomorphisms whose right adjoints preserve multiplication ∗, it is proved that E-projective quantales are exactly weakly ∗-stable completely distributive lattices. It is also proved that there are no nontrivial injective objects in the category of quantales