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.
Theory and Applications of Categories, Vol. 6, 1999, No. 5, pp 65-76 http://www.tac.mta.ca/tac/volumes/6/n5/n5.dvi http://www.tac.mta.ca/tac/volumes/6/n5/n5.ps ftp://ftp.tac.mta.ca/pub/tac/html/volumes/6/n5/n5.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/6/n5/n5.psTAC Home