  We provide a general method for constructing moduli stacks whose points are
diagrams of vector bundles over a fixed base, indexed by a fixed simplicial set
-- that is, quiver bundles of a fixed shape. We discuss some constraints on the
base for these moduli stacks to be algebraic and observe that a large class of
interesting schemes satisfy these constraints. Using this construction, we
provide an alternate construction of moduli stacks of Higgs bundles along with
a proof of algebraicity following readily from the algebraicity of moduli
stacks of quiver bundles. One feature of our approach is that, for each of the
moduli stacks we discuss, there are algebraic moduli stacks parametrizing
morphisms of the objects being classified. We discuss some potential
applications of this in categorifying non-abelian Hodge theory in a sense we
will make precise. We also discuss potential applications of our methods and
perspectives to the subjects of quiver modifications, abstract moduli theory,
and homotopy theory.
