Morphism of algebraic stacks

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In algebraic geometry, given algebraic stacks ${\displaystyle p:X\to C,\,q:Y\to C}$ over a base category C, a morphism ${\displaystyle f:X\to Y}$ of algebraic stacks is a functor such that ${\displaystyle q\circ f=p}$.

More generally, one can also consider a morphism between prestacks (a stackification would be an example).