  Given a diagram of schemes, we can ask if a geometric object over one of them
can be built from descent data (usually objects of the same type over the
various other schemes in the diagram, together with compatibility
isomorphisms). Using the language of moduli stacks, we can rephrase this as
follows: saying that descent problems for a given diagram have essentially
unique solutions amounts to saying that the diagram in question is a
(bicategorical) colimit diagram in a certain 2-category of stacks.
  In this paper we use generalized Tannaka duality to explicitly compute
certain colimits in the 2-category of Adams stacks. Using this we extend recent
results of Bhatt from algebraic spaces to Adams stacks and a result of
Hall-Rydh to non-noetherian rings.
  We conclude the paper with a global version of the Beauville-Laszlo theorem,
which states that a large class of schemes and stacks can be built by gluing
the open complement of an effective Cartier divisor with the infinitesimal
neighbourhood of the divisor.
