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  "body": "\n## Summary\n\nA sieve on an object $c$ of a [[category|A2DE66937D]] is a collection of morphisms with codomain $c$ that is closed under composition on the right.\nEquivalently, it is a subfunctor of the [[representable functor|KCCHH87H6E]] $\\Hom(-, c)$.\nSieves are the building blocks of [[Grothendieck topologies|GDRFSJ8E2B]]: a Grothendieck topology chooses which sieves count as coverings.\nThey play the role of open covers in a topological space.\n\n## Explanations\n\n### L1 human\n\nThink of $c$ as an open set and of morphisms $d \\to c$ as smaller open sets inside it.\nA sieve on $c$ is a family of such smaller sets that is closed under shrinking.\nIf $V$ is in the family and $W \\subseteq V$ is open, then $W$ is in the family too.\nFor example, for an open cover $\\set{U_i}$ of $U$, all open sets contained in some $U_i$ form a sieve on $U$.\nWorking with sieves rather than covers removes the choice of a particular list of sets.\n",
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