  We introduce categories of weak factorization algebras and factorization
spaces, and prove that they are equivalent to the categories of ordinary
factorization algebras and spaces, respectively. This allows us to define the
pullback of a factorization algebra or space by an \'etale morphism of schemes,
and hence to define the notion of a universal factorization space or algebra.
This provides a generalization to higher dimensions and to non-linear settings
of the notion of a vertex algebra.
