  We extend the construction of the normal cone of a closed embedding of
schemes to any locally of finite type morphism of higher Artin stacks and show
that in the Deligne-Mumford case our construction recovers the relative
intrinsic normal cone of Behrend and Fantechi. We characterize our extension as
the unique one satisfying a short list of axioms, and use it to construct the
deformation to the normal cone. As an application of our methods, we associate
to any morphism of Artin stacks equipped with a choice of a global perfect
obstruction theory a relative virtual fundamental class in the Chow group of
Kresch.
