Contravariant Functors on Finite Sets and Stirling Numbers

Robert Paré

We characterize the numerical functions which arise as the cardinalities of contravariant functors on finite sets, as those which have a series expansion in terms of Stirling functions. We give a procedure for calculating the coefficients in such series and a concrete test for determining whether a function is of this type. A number of examples are considered.

Keywords: Functor, cardinality, Stirling numbers.

1991 MSC: 18A22, 05A10.

Theory and Applications of Categories, Vol. 6, 1999, No. 5, pp 65-76.

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