Let K be the structure got by forgetting the composition law of morphisms in a given category. A linear representation of is given by a map V associating with any morphism ~ : a -~e of K a linear vector space map V(~) : V(a) -~V(e). We classify those K having only finitely many isomorphy classes of indecomposable linear representations. This classification is related to an old paper by Yoshii [3].i. Einleitung.
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