  In this paper, we continue the study of the category of functors Fquad,
associated to F_2-vector spaces equipped with a nondegenerate quadratic form,
initiated in two previous papers of the author. We define a filtration of the
standard projective objects in Fquad; this refines to give a decomposition into
indecomposable factors of the two first standard projective objects in Fquad.
As an application of these two decompositions, we give a complete description
of the polynomial functors of the category Fquad.
