  We prove that, in the category F of functors between F\_2-vector spaces, the
tensor product between the second non constant standard injective functor and
an exterior power functor is artinian. The only cas known to date was the
artinian character of this injective ; our result is a step in the study of the
third non constant standard injective. We use the division functor by the
identity functor and facts from modular representation theory of the symmetric
groups to obtain this theorem by detecing suitable composition factors.
