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A Zariski cover of a scheme $T$ is a family of open immersions $(j_i:U_i\hookrightarrow T{)}_{i\in I}$ whose images cover its underlying topological space:There is no finiteness requirement. Intersections used in the sheaf on a site condition are the pullbacks $U_i{\times }_T{U}_j$, identified with the corresponding open subschemes $U_i\cap U_j$.

A Grothendieck topology is subcanonical when every representable functor is a sheaf on a site. It is also called standard in some topos-theory terminology. A nontrivial covering quotient can fail this condition by identifying distinct sections of a representable.