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  "body": "\n## Definition\n\nA *site* is a pair $(\\mathcal{C}, J)$, where $\\mathcal{C}$ is a [[category|A2DE66937D]] and $J$ is a [[Grothendieck topology|GDRFSJ8E2B]] on $\\mathcal{C}$.\nThe site is *small* when $\\mathcal{C}$ is a small category.\n\n## Remarks\n\nExample: for a topological space $X$, let $\\mathcal{O}(X)$ be the category of open sets with inclusions.\nLet a sieve on $U$ cover when the union of its members is $U$.\nThis rule satisfies the three axioms of a Grothendieck topology, so $(\\mathcal{O}(X), J)$ is a small site.\nNon-example: the category $\\mathcal{O}(X)$ alone, with no choice of covering sieves, is not a site, since it does not say which families cover.\nSome authors define a site with a Grothendieck pretopology, that is, with covering families of morphisms instead of covering sieves; each pretopology determines a topology with the same sheaves.\n",
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    "name": "Site",
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  "name": "Site",
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/YMK/YMK0D06F4B.md",
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      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
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        "what": "a source with a locator",
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