  We study descent properties of Jacob Lurie's topological chiral homology. We
prove that this homology theory satisfies descent for a factorizing cover, as
defined by Kevin Costello and Owen Gwilliam. We also obtain a generalization of
Lurie's approach to this homology theory, which leads to a product formula for
the infinity $1$-category of factorization algebras, and its twisted
generalization.
