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.
Theory and Applications of Categories, Vol. 10, 2002, No. 18, pp 461-468 http://www.tac.mta.ca/tac/volumes/10/18/10-18.dvi http://www.tac.mta.ca/tac/volumes/10/18/10-18.ps http://www.tac.mta.ca/tac/volumes/10/18/10-18.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/18/10-18.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/18/10-18.psTAC Home