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'functorial morphisms'
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| Title of object: |
functorial morphisms |
| Canonical Name: |
FundamentalGroupoid2 |
| Type: |
Definition |
| Created on: |
2008-07-20 09:39:54 |
| Modified on: |
2008-07-25 13:24:49 |
| Classification: |
msc:18A25, msc:18-00, msc:55R37, msc:55R65, msc:55R10, msc:55P99 |
| Keywords: |
morphism of a functor category, natural transformation, functor categories, natural transformations |
| Defines: |
transformations, morphisms between functors, morphism in the 2--category of functors |
| Synonyms: |
functorial morphisms=natural transformations |
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Content:
\textbf{'functorial morphisms'} is another name for \emph{natural transformations} 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, viz. (ref. \cite{CE1965}).
\begin{thebibliography}{9}
\bibitem{Ha}A. Hatcher, \emph{Algebraic Topology}, Cambridge University Press, 2002.
\bibitem{Ma}S. Mac Lane, \emph{Categories for the Working Mathematician} (2nd edition), Springer-Verlag, 1997.
\bibitem{EC1966}
C. Ehresmann, Trends Toward Unity in Mathematics., \emph{Cahiers de Topologie et Geometrie Differentielle}
\textbf{8}: 1-7, 1966.
\bibitem{CE1965}
C. Ehresmann, \emph{Cat\'egories et Structures}. Dunod: Paris , 1965.
\bibitem{Eh-quintettes}
C. Ehresmann, Cat\'egories doubles des quintettes: applications covariantes
, \emph{C.R.A.S. Paris}, \textbf{256}: 1891-1894, 1963.
\bibitem{Eh-Oe}
C. Ehresmann, \emph{Oeuvres compl\`etes et comment\'ees:
Amiens, 1980-84}, 1984 (\emph{edited and commented by Andr\'ee Ehresmann}).
\bibitem{EML1}
S. Eilenberg and S. Mac Lane., Natural Isomorphisms in Group Theory., \emph{American Mathematical Society 43}: 757-831, 1942.
\bibitem{EML45}
S. Eilenberg and S. Mac Lane, The General Theory of Natural Equivalences, \emph{Transactions of the American Mathematical Society} \textbf{58}: 231-294, 1945.
\bibitem{Gabriel1962}
P. Gabriel, Des cat\'egories ab\'eliennes, \emph{Bull. Soc.Math. France}
\textbf{90}: 323-448, 1962.
\bibitem{Alex3}
A. Grothendieck, and J. Dieudon\'{e}, \emph{El\'{e}ments de geometrie alg\'{e}brique.}, \emph{Publ. Inst. des Hautes Etudes de Science}, \textbf{4}, 1960.
\bibitem{NP1973}
N. Popescu, \emph{Abelian Categories with Applications to Rings and Modules.}, New York and London: Academic Press.,
1973, 2nd edn. 1975, \emph{(English translation by I.C. Baianu)}.
\end{thebibliography} |
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