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  "body": "\n## Summary\n\nThe opposite category $\\mathcal{C}^{\\mathrm{op}}$ of a [[category|A2DE66937D]] $\\mathcal{C}$ has the same objects and the same morphisms, with every arrow reversed.\nIt turns [[monomorphisms|Y2NP1JFR86]] into [[epimorphisms|RVXDSY04KG]], products into coproducts, and limits into colimits.\nIt is the basis of [[duality in category theory|Z5EETTFWAN]].\nIt also lets one write a [[contravariant functor|RECR96V97B]] on $\\mathcal{C}$ as an ordinary functor on $\\mathcal{C}^{\\mathrm{op}}$.\n\n## Explanations\n\n### L1 human\n\nTake a drawing of a category and reverse the direction of every arrow.\nThe result is again a category, because chains of arrows can still be composed, in the reverse order.\nFor a [[preorder|0VABYWJWH9]] seen as a category, with an arrow $a \\to b$ when $a \\le b$, the opposite category is the reversed order $\\ge$.\nFor the numbers $1 \\le 2 \\le 3$, the opposite category has arrows $3 \\to 2 \\to 1$.\n",
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