On the Mittag-Leffler Property

ABSTRACT

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 )β α 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.