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Polynomial functors

A polynomial functor (of one variable) is an endofunctor of the category of sets, built from disjoint unions, products, and exponentiation. They are the categorification of polynomials with natural-number coefficients, and many constructions and results about such polynomials of numbers can be explained on the level of polynomials of sets, e.g. basic constructions like sums, products, substitutions, differentiation, and their basic properties, like the Leibniz rule and the chain rule. Just as for polynomials you can perform many manipulations solely in terms of the coefficients, the operations on polynomial functors can be performed in terms of sets. The theory of polynomial functors has applicatons to combinatorics, type theory, topology, operads and higher category theory.

I recommend instead the papers listed below.

See also the page on Combinatorics of graphs and trees in perturbative quantum field theory

Last updated: 2013-01-10 by Joachim Kock.