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  "body": "\n## Summary\n\nThe category of posets, written $\\mathbf{Pos}$, has the [[partially ordered sets|011C29Q1S1]] as objects and the [[monotone functions|0WFF6AZPBP]] as morphisms.\nIts isomorphisms are the [[order isomorphisms|0Y74KN99A5]].\nIt sits inside the larger category of preordered sets, and it lets order theory use the language of [[category theory|Q1RZT7DV0F]].\n\n## Explanations\n\n### L1 human\n\nThe category of posets collects all ordered sets and all maps that respect order.\nTwo such maps compose to another map that respects order, and the identity map respects order.\nFor example, $n \\mapsto 2n$ from $\\N$ to $\\N$ and the inclusion of $\\N$ into $\\Z$ compose to a monotone map from $\\N$ to $\\Z$.\nTreating posets this way makes products, sums and other constructions on orders into special cases of general constructions.\n",
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