functorial morphism
Functorial morphism is another name for natural transformation which was, and still is, employed especially in the context of category theory and applications developed by Charles Ehresmann, the ‘Nicolas Bourbaki’ group and other French schools of mathematics; this is also a natural, English translation of the same concept from French, that is a ‘morphism between functors’, viz. (ref. [4]).
References
- 1 A. Hatcher, Algebraic Topology, Cambridge University Press, 2002.
- 2 S. Mac Lane, Categories 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 Structures. 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 Categories 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 | morphism 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 |