  We show that the weakly \'etale morphisms, used to define the pro-\'etale
site of a scheme, are characterized by a lifting property similar to the one
which characterizes formally \'etale morphisms. In order to prove this, we
prove a theorem called Henselian descent which is a "Henselized version" of the
fact that a scheme defines a sheaf for the fpqc topology. Finally, we show that
weakly \'etale algebras over regular rings arising in geometry are ind-\'etale
and that weakly \'etale algebras do not always lift along surjective ring
homomorphisms.
