There is a categorical interpretation of this construction. Let be the category of integral domains and injective ring maps. The functor from to the category of fields that takes every integral domain to its fraction field and every homomorphism to the induced map on fields (which exists by the universal property) is the left adjoint of the inclusion functor from the category of fields to . Thus the category of fields (which is a full subcategory) is a reflective subcategory of .
There is a categorical interpretation of this construction. Let be the category of integral domains and injective ring maps. The functor from to the category of fields that takes every integral domain to its fraction field and every homomorphism to the induced map on fields (which exists by the universal property) is the left adjoint of the inclusion functor from the category of fields to . Thus the category of fields (which is a full subcategory) is a reflective subcategory of 