For any scheme "X", let Ét("X") be the category of all étale morphisms from a scheme to "X". This is the analog of the category of open subsets of "X" (that is, the category whose objects are varieties and whose morphisms are open immersions). Its objects can be informally thought of as étale open subsets of "X". The intersection of two objects corresponds to their fiber product over "X". Ét("X") is a large category, meaning that its objects do not form a set.