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]).

Bibliography

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2

S. Mac Lane, Categories for the Working Mathematician (2nd edition), Springer-Verlag, 1997.

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C. Ehresmann, Trends Toward Unity in Mathematics., Cahiers de Topologie et Geometrie Differentielle 8: 1-7, 1966.

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6

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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).