  We provide a toolbox of extension, gluing, and assembly techniques for
factorization algebras.
  Using these tools, we fill various gaps in the literature on factorization
algebras on stratified manifolds, the main one being that constructible
factorization algebras form a sheaf of symmetric monoidal $\infty$-categories.
Additionally, we explain how to assemble constructible factorization algebras
from the data on the individual strata together with module structures
associated to the relative links; thus answering a question by Ayala.
  Along the way, we give detailed proofs of the following facts which are also
of independent interest: constructibility is a local condition; the
$\infty$-category of disks is a localization of any sufficiently fine poset of
disks; constructibility implies the Weiss condition on disks. For each of
these, variants or special cases already existed, but they were either
incomplete or not general enough.
