 A stack is called a stack in groupoids or a (2,1)-sheaf if it is also fibered in groupoids, meaning that its fibers (the inverse images of objects of "C") are groupoids.Some authors use the word "stack" to refer to the more restrictive notion of a stack in groupoids.An algebraic stack or Artin stack is a stack in groupoids "X" over the etale site such that the diagonal map of "X" is representable and there exists a smooth surjection from (the stack associated to) a scheme to X.