  We explain how any Artin stack $\mathfrak{X}$ over $\mathbb{Q}$ extends to a
functor on non-negatively graded commutative cochain algebras, which we think
of as functions on Lie algebroids or stacky affine schemes. There is a notion
of \'etale morphisms for these CDGAs, and Artin stacks admit \'etale atlases by
stacky affines, giving rise to a small \'etale site of stacky affines over
$\mathfrak{X}$. This site has the same quasi-coherent sheaves as $\mathfrak{X}$
and leads to efficient formulations of shifted Poisson structures, differential
operators and quantisations for Artin stacks. There are generalisations to
higher and derived stacks.
  We also describe analogues for differentiable and analytic stacks; in
particular, a Lie groupoid naturally gives a functor on NQ-manifolds which we
can use to transfer structures. In those settings, local diffeomorphisms and
biholomorphisms are the analogues of \'etale morphisms.
  This note mostly elaborates constructions scattered across several of the
author's papers, but with an emphasis on the functor of points perspective. New
results include consistency checks showing that the induced notions of
structures such as vector bundles or torsors on a stacky affine scheme coincide
with familiar definitions in terms of flat connections.
