over a base category C, a morphism
of algebraic stacks is a functor such that
More generally, one can also consider a morphism between prestacks (a stackification would be an example).
One particular important example is a presentation of a stack, which is widely used in the study of stacks.
An algebraic stack X is said to be smooth of dimension n - j if there is a smooth presentation
denotes the moduli stack of rank-n vector bundles, then there is a presentation
A quasi-affine morphism between algebraic stacks is a morphism that factorizes as a quasi-compact open immersion followed by an affine morphism.
[1] This algebraic geometry–related article is a stub.