In fact "a" is the adjoint functor to the inclusion functor from the category of sheaves to the category of presheaves, and "i" is the unit of the adjunction.By this way, the category of sheaves turns into Giraud subcategory of presheaves.
In fact "a" is the adjoint functor to the inclusion functor from the category of sheaves to the category of presheaves, and "i" is the unit of the adjunction. In this way, the category of sheaves turns into Giraud subcategory of presheaves.