Smooth stack

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; for this, see prestack#Morphisms (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.

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