On the Mittag-Leffler Property
نویسنده
چکیده
Let C be a category with strong monomorphic strong coimages, that is, every morphism ƒ of C factors as ƒ = u ° g so that g is a strong epimorphism and u is a strong monomorphism and this factorization is universal. We define the notion of strong Mittag-Leffler property in pro-C. We show that if ƒ : X → Y is a level morphism in pro-C such that ( ) p Y ! " is a strong epimorphism for all β > α, then X has the strong Mittag-Leffler property provided ƒ is an isomorphism. Also, if ƒ : X → Y is a strong epimorphism of pro-C and X has the strong Mittag-Leffler property, we show that Y has the strong Mittag-Leffler property. Moreover, we show that this property is invariant of isomorphisms of pro-C.
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