An étale presheaf on "X" is a contravariant functor from Ét("X") to the category of sets. A presheaf "F" is called an étale sheaf if it satisfies the analog of the usual gluing condition for sheaves on topological spaces. That is, "F" is an étale sheaf if and only if the following condition is true. Suppose that is an object of Ét("X") and that is a jointly surjective family of étale morphisms over "X". For each "i", choose a section "x""i" of "F" over "U""i". The projection map , which is loosely speaking the inclusion of the intersection of "U""i" and "U""j" in "U""i", induces a restriction map . If for all "i" and "j" the restrictions of "x""i" and "x""j" to are equal, then there must exist a unique section "x" of "F" over "U" which restricts to "x""i" for all "i".