A species of structures is a rule which
1. Produces, for each finite set , a finite set ,
2. Produces, for each bijection , a function
(1)
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The functions should further satisfy the following functorial properties:
1. For all bijections and ,
(2)
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2. For the identity map ,
(3)
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An element is called an -structure on (or a structure of species on ). The function is called the transport of -structures along .