Geodesic
Contravariant Functors on Finite Sets and Stirling Numbers
Theory and applications of categories, The Lambek Festschrift, Tome 6 (1999), pp. 65-76
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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.

Classification : 18A22, 05A10.
Keywords: Functor, cardinality, Stirling numbers. 
@article{TAC_1999_6_a4,
     author = {Robert Par\'e},
     title = {Contravariant {Functors} on {Finite} {Sets} and {Stirling} {Numbers}},
     journal = {Theory and applications of categories},
     pages = {65--76},
     year = {1999},
     volume = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1999_6_a4/}
}
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Robert Paré. Contravariant Functors on Finite Sets and Stirling Numbers. Theory and applications of categories, The Lambek Festschrift, Tome 6 (1999), pp. 65-76. http://geodesic.mathdoc.fr/item/TAC_1999_6_a4/