  In 1994, Long and Moody gave a construction on representations of braid
groups which associates a representation of \mathbf{B}\_{n} with a
representation of \mathbf{B}\_{n+1}. In this paper, we prove that this
construction is functorial and can be extended: it inspires endofunctors,
called Long-Moody functors, between the category of functors from Quillen's
bracket construction associated with the braid groupoid to a module category.
Then we study the effect of Long-Moody functors on strong polynomial functors:
we prove that they increase by one the degree of very strong polynomiality.
