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  "body": "\n## Summary\n\nA combinatorial species is a rule that assigns to each finite set the structures of a given kind on it, see the [[definition|K9VZKJACKT]].\nThe rule must be compatible with renaming the elements, which makes it a functor on finite sets and bijections.\nEach species has an [[exponential generating function|0JHXPVFKT0]], and operations on species match operations on these series.\nThe theory was introduced by André Joyal and gives a conceptual basis for the [[symbolic method|JP11D90EJC]] for labelled structures.\n\n## Explanations\n\n### L1 human\n\nThink of a kind of structure, such as \"a linear order\", \"a graph\" or \"a rooted tree\", that you can put on any set of labels.\nThe species records, for each set of labels, all such structures on it.\nRenaming the labels moves structures to structures, in a consistent way.\nFor example, the species of linear orders gives $n!$ structures on a set of $n$ labels, and the species of graphs gives $2^{\\binom{n}{2}}$.\n",
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