Uniqueness of monogeny classes for uniform objects in abelian categories

We show that if A1,A2,…,An,B1,B2,…,Bt are uniform objects of an abelian category C, then A1circled plusA2circled pluscdots, three dots, centeredcircled plusAn and B1circled plusB2circled pluscdots, three dots, centeredcircled plusBt are in the same monogeny class if and only if n=t and there is a permutation σ of {1,2,…,n} such that Ai and Bσ(i) are in the same monogeny class for every i=1,2,…,n. This is proved by showing that strong components of bipartite digraphs with enough edges intersect the two independent sets of vertices of a bipartition of the digraph in sets of the same cardinality.