  This notes aims to clarify the proof given by Raynaud and Gruson that the
Mittag-Leffler property descents via pure rings monomorphism of commutative
rings. A consequence of that is that projectivity dencents via such ring
homomorphisms, a revision of the proof also allows to prove that the property
of being pure-projective also descents via pure monomorphisms between
commutative rings}.
