Generic morphisms, parametric representations and weakly cartesian monads
Theory and applications of categories, The Carboni Festschrift, Tome 13 (2004), pp. 191-234.

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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.
Classification : 18D50, 55P48
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     author = {Mark Weber},
     title = {Generic morphisms, parametric representations
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     volume = {13},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2004_13_a13/}
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Mark Weber. Generic morphisms, parametric representations
and weakly cartesian monads. Theory and applications of categories, The Carboni Festschrift, Tome 13 (2004), pp. 191-234. http://geodesic.mathdoc.fr/item/TAC_2004_13_a13/