The structure of the tensor product of 𝔽 2 [ - ] with a finite functor between 𝔽 2 -vector spaces

The paper studies the structure of functors I ⊗ 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 ↦ 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 ⊗ F are artinian of type one.