functorial morphism

Functorial morphismPlanetmathPlanetmath is another name for natural transformation which was, and still is, employed especially in the context of category theoryMathworldPlanetmathPlanetmathPlanetmathPlanetmath and applications developed by Charles Ehresmann, the ‘Nicolas Bourbaki’ group and other French schools of mathematics; this is also a natural, English translationMathworldPlanetmathPlanetmath of the same concept from French, that is a ‘morphism between functors’, viz. (ref. [4]).


  • 1 A. Hatcher, Algebraic Topology, Cambridge University Press, 2002.
  • 2 S. Mac Lane, CategoriesMathworldPlanetmath for the Working Mathematician (2nd edition), Springer-Verlag, 1997.
  • 3 C. Ehresmann, Trends Toward Unity in Mathematics., Cahiers de Topologie et Geometrie Differentielle 8: 1-7, 1966.
  • 4 C. Ehresmann, Catégories et StructuresMathworldPlanetmath. Dunod: Paris , 1965.
  • 5 C. Ehresmann, Catégories doubles des quintettes: applications covariantes , C.R.A.S. Paris, 256: 1891-1894, 1963.
  • 6 C. Ehresmann, Oeuvres complètes et commentées: Amiens, 1980-84, 1984 (edited and commented by Andrée Ehresmann).
  • 7 S. Eilenberg and S. Mac Lane., Natural Isomorphisms in Group Theory., American Mathematical Society 43: 757-831, 1942.
  • 8 S. Eilenberg and S. Mac Lane, The General Theory of Natural Equivalences, Transactions of the American Mathematical Society 58: 231-294, 1945.
  • 9 P. Gabriel, Des catégories abéliennes, Bull. Soc.Math. France 90: 323-448, 1962.
  • 10 A. Grothendieck, and J. Dieudoné, Eléments de geometrie algébrique., Publ. Inst. des Hautes Etudes de Science, 4, 1960.
  • 11 N. Popescu, Abelian CategoriesMathworldPlanetmathPlanetmathPlanetmath with Applications to Rings and Modules., New York and London: Academic Press., 1973, 2nd edn. 1975, (English translation by I.C. Baianu).
Title functorial morphism
Canonical name FunctorialMorphism
Date of creation 2013-03-22 18:14:53
Last modified on 2013-03-22 18:14:53
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 20
Author bci1 (20947)
Entry type Feature
Classification msc 55P99
Classification msc 55R10
Classification msc 55R65
Classification msc 55R37
Classification msc 18A05
Classification msc 18A25
Classification msc 18-00
Synonym morphisms between functors
Synonym morphismMathworldPlanetmath in the 2–category of functorsnatural transformations
Related topic NaturalTransformation
Related topic FundamentalGroupoidFunctor
Related topic Monad
Related topic EilenbergMacLaneSpace
Related topic Sheaf2
Related topic FundamentalGroupoid
Related topic HomotopyDoubleGroupoidOfAHausdorffSpace
Defines transformations