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  "body": "\n## Summary\n\nThe product order on a [[Cartesian product|09CEDJYBKP]] of partially ordered sets compares tuples coordinate by coordinate.\nOne tuple is below another when each of its coordinates is below the matching coordinate.\nIt is the product in the category of posets, and products of chains are the model spaces for [[order dimension|JC4J24MF93]].\n\n## Explanations\n\n### L1 human\n\nCompare two students by their marks in two subjects.\nSay that the first is behind the second when the first scored at most as well in both subjects.\nA student with marks $(70, 80)$ is behind one with $(75, 90)$, but $(70, 90)$ and $(75, 80)$ cannot be compared.\nSo the product of two total orders is usually not a total order.\n",
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      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
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      {
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