Sieve

Summary

A sieve on an object $c$ of a category is a collection of morphisms with codomain $c$ that is closed under composition on the right. Equivalently, it is a subfunctor of the representable functor $\Hom(-, c)$. Sieves are the building blocks of Grothendieck topologies: a Grothendieck topology chooses which sieves count as coverings. They play the role of open covers in a topological space.