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The paper studies the structure of functors $I\otimes F$ in the category of functors from finite dimensional ${𝔽}_2$-vector spaces to ${𝔽}_2$-vector spaces, where $F$ is a finite functor and $I$ is the injective functor $V\mapsto {𝔽}_2^{V^{*}}$. A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors $I\otimes F$ are artinian of type one.