Given two d-dimensional Λ-modules M and N, then M degenerates to N if and only if there exists an exact sequence of the form 0→ U→ U ⊕ M→ N→ 0 for some U ∈ mod Λ (Zwara, 1998). Having this as a starting point, in this article we give a characterization of degenerations by the existence of a certain finitely presented functor. This gives new information about U in the sequence above. We show how this new information can be used to prove that M ≰ degN even when M ⊕ X ≤ degN ⊕ X for some X for modules over Λq = k〈 x,y〉/〈 x2,y2,xy + qyx〉, q ≠ 0 in k, where k is an algebraically closed field.
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