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What is a prestack?

What is a prestack? Here are some definitions.

Noun
  1. (category theory) The category c is called a prestack over a category C with a Grothendieck topology if it is fibered over C and for any object U of C and objects x, y of c with image U, the functor from objects over U to sets taking F:V→U to Hom(F*x,F*y) is a sheaf.
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