Calculus of Species
Arithmetic on generating functions corresponds to certain "natural" operations on species. The basic operations are addition, multiplication, composition, and differentiation; it is also necessary to define equality on species. Category theory already has a way of describing when two functors are equivalent: a natural isomorphism. In this context, it just means that for each A there is a bijection between F-structures on A and G-structures on A, which is "well-behaved" in its interaction with transport. Species with the same generating function might not be isomorphic, but isomorphic species do always have the same generating function.
Read more about this topic: Combinatorial Species
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“I try to make a rough music, a dance of the mind, a calculus of the emotions, a driving beat of praise out of the pain and mystery that surround me and become me. My poems are meant to make your mind get up and shout.”
—Judith Johnson Sherwin (b. 1936)
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