A similarity relation s1 is an equivalence relation and induces an equivalence partitioning X/s1 on the domain X. Similarly, a similarity relation s2 is an equivalence relation and induces an equivalence partitioning Y/s2 on the domain Y. What we are saying is that the homological image of X/s1 is a refinement of Y/s2. In other words, if X1 of X is an equivalence set and f(X1) its homological image, then f(X1) must be contained in some equivalence set Y2 of Y. In fact, this procedure can be used to effectively determine wither f is a type-M dependency relation, when the cardinality of the equvalence partitioning is finite for both similarity relations.