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  "body": "\n## Summary\n\nAn embedding of one [[structure|983GZBQYT4]] into another is an injective [[homomorphism|KBXSZC6BV1]] that also reflects the relations.\nIt identifies the first structure with a [[substructure|676H7EGTKJ]] of the second, up to [[isomorphism|PZMGQMDN25]].\nEmbeddings let one say that a structure \"sits inside\" another, as $\\Z$ sits inside $\\Q$.\n[[Elementary embeddings|CGH8C8EA9N]] are the embeddings that preserve all first-order formulas.\n\n## Explanations\n\n### L1 human\n\nAn embedding places a copy of one structure inside another without losing any information.\nThe map that sends an integer $n$ to the rational number $n/1$ is an embedding of the ring of integers into the field of rational numbers.\nDifferent elements go to different elements, sums go to sums and products go to products.\nFor relational structures, such as graphs, an embedding must also keep non-edges as non-edges.\n",
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