Reflective subcategories

@article{Rada2000ReflectiveS,
  title={Reflective subcategories},
  author={Juan Rada and Manuel Saori{\^a} and Alberto del Valle},
  journal={Glasgow Mathematical Journal},
  year={2000},
  volume={42},
  pages={97 - 113}
}
Given a full subcategory [Fscr ] of a category [Ascr ], the existence of left [Fscr ]-approximations (or [Fscr ]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that [Fscr ] is reflective in [Ascr ], in the classical terminology of category theory. In the first part of the paper we establish, for a rather general [Ascr ], the relationship between reflectivity and covariant finiteness of [Fscr ] in [Ascr ], and generalize Freyd's adjoint functor theorem (for inclusion… 
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