Given a triple T on a complete category C and a factorization system E/M on the category of algebras, we show there is a 1-1 correspondence between full subcategories of the category of algebras that are closed under U-split epimorphisms, products, and M-subobjects and triple morphisms T -> S for which the induced natural transformation between free functors belongs to E.
Keywords: Birkhoff subcategories, factorizations, reflective subcategories.
2000 MSC: 18C05, 18A20, 18A40.
Theory and Applications of Categories, Vol. 10, 2002, No. 18, pp 461-468.
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