Starting in 2009, Harbater and Hartmann introduced a new patching setup
for semi-global fields, establishing a patching framework for vector spaces, central
simple algebras, quadratic forms and other algebraic structures. In subsequent
work with Krashen, the patching framework was refined and extended to
torsors and certain Galois cohomology groups. After describing this framework,
we will discuss an extension of the patching equivalence to bitorsors and gerbes.
Building up on these results, we then proceed to derive a characterisation of a local-
global principle for gerbes and bitorsors in terms of factorization. These results can be
expressed in the form of a Mayer-Vietoris sequence in non-abelian hypercohomology
with values in the crossed-module $G->Aut(G)$. After proving the local-global
principle for certain bitorsors and gerbes using the characterization mentioned above,
we conclude with an application on rational points for homogeneous spaces.