Abstract
Morphisms of functors or natural transformations between functors of different variance are investigated. In order to be able to define the usual compositions of morphisms of functors in this case, too, and to formulate the corresponding results smoothly, one is forced to define a morphism of functors essentially as a mapping from one category to another and not as usual as a mapping from the class of objects of one category to another category. Two new invariants of a morphism of functors, the parity and the exponent, arise in a natural way and are the main tools in proving all the results.
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Literatur
BÉNABOU, J.: Catégories avec multiplication, C.R. Acad. Sci. Paris 256, 1887–1890 (1963).
BÉNABOU, J.: Algèbre élémentaire dans les catégories avec multiplication, C.R. Acad. Sci. Paris 258, 771–774 (1964).
BÉNABOU, J.: Catégories relatives, C.R. Acad. Sci. Paris 260, 3824–3827 (1965).
BÉNABOU, J.: Introduction to bicategories, Reports of the Midwest Category Seminar, Lecture Notes, 1–77, Berlin-Heidelberg-New York Springer (1967).
BOURBAKI, N.: Théorie des ensembles, chap. 4, Paris, Hermann (1957).
GODEMENT, R.: Théorie des faisceaux, Paris, Hermann (1958).
KAN, D.M.: Adjoint functors, Trans. Am. Math. Soc. 87, 294–329 (1958).
MAC LANE, S.: Categorical algebra, Bull. Am. Math. Soc. 71, 40–106 (1965).
SONNER, J.: Universal and special problems, Math.Z. 82, 200–211 (1963).
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Research partially supported by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 68-1572.
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Pumplün, D., Röhrl, H. Morphismen von Funktoren. Manuscripta Math 1, 87–98 (1969). https://doi.org/10.1007/BF01171136
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DOI: https://doi.org/10.1007/BF01171136