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.