Giraud subcategory

In mathematics, Giraud subcategories form an important class of subcategories of Grothendieck categories. They are named after Jean Giraud.
Definition.
Let formula_1 be a Grothendieck category. A full subcategory formula_2 is called "reflective", if the inclusion functor formula_3 has a left adjoint. If this left adjoint of formula_4 also preserves 
kernels, then formula_2 is called a "Giraud subcategory".
Properties.
Let formula_2 be Giraud in the Grothendieck category formula_1 and formula_3 the inclusion functor.