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Composing special epimorphisms and retractions. (English) Zbl 0941.18003

The authors demonstrate the bad composition behaviour of regular and of extremal epimorphisms in some concrete categories: in the category of small categories, the composite of a regular epimorphism followed by a retraction need not be regular, and in some supercategory of \({\mathcal C}at\) one may replace “regular” by “extremal” in this statement; furthermore, in the category of (non-empty) connected topological spaces, the composite of a retraction followed by a regular epimorphism need not be regular.
[These observations complement nicely corresponding remarks made at the end of R. Börger’s paper on “Making factorizations compositive”, Commentat. Math. Univ. Carol. 32, No. 4, 749-759 (1991; Zbl 0760.18001)].

MSC:

18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms

Citations:

Zbl 0760.18001
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References:

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