Covering Sieve

A covering sieve is a component of a Grothendieck topology that forms a collection of sieves $J(X)$ for each object $X$ such that:

• Stability: The pullback of a covering sieve along an arbitrary morphisms is itself a ccovering sieve.
• Local character: If a sieve $S$ containers a covering sieve $J^{\prime }$ after pulling back then $S$ is itself a covering sieve.