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We provide necessary and/or sufficient conditions for the stable Hom functorsto be finitely presented. A notion of defect of an arbitrary additive functoron a module category is introduced. The defect of the covariant Hom functormodulo projectives is shown to be isomorphic to the Bass torsion of the fixedargument. The defect of the contravariant Hom functor modulo injectives isshown to be isomorphic to the cotorsion coradical of the fixed argument.

The finite presentation of the stable Hom functors, the Bass torsion, and the cotorsion coradical