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  "body": "\n## Summary\n\nA class of structures has the amalgamation property when any two members that share a common part fit together in a third member.\nIn the third member, the two copies of the common part must coincide.\nIt is one of the three conditions in Fraïssé's theorem, which builds a countable homogeneous structure, the [[Fraïssé limit|HJVRBDQSGG]], from a class of finite structures.\nIt also appears in algebra, for example in the study of amalgamated free products of groups.\n\n## Explanations\n\n### L1 human\n\nThink of two drawings that both contain the same small picture.\nAmalgamation means one can draw a bigger picture that contains both drawings and in which the two copies of the small picture are the same.\nFor finite graphs this is easy: take two graphs $B$ and $C$ that both contain a graph $A$, glue them along $A$, and add no other edges.\nThe glued graph contains $B$ and $C$, and the two copies of $A$ coincide.\n",
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