Two notions, generic morphisms and parametric representations, useful for the analysis of endofunctors arising in enumerative combinatorics, higher dimensional category theory, and logic, are defined and examined. Applications to the Batanin approach to higher category theory, Joyal species and operads are provided.
2000 MSC: 18D50, 55P48
Theory and Applications of Categories,
Vol. 13, 2004,
No. 14, pp 191-234.
http://www.tac.mta.ca/tac/volumes/13/14/13-14.dvi
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http://www.tac.mta.ca/tac/volumes/13/14/13-14.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/13/14/13-14.dvi
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