Abstract
We study direct product decompositions of objects in a finitely complete and cocomplete category with zero object and certain axioms for a coimage factorization of morphisms. Direct productsC=A×B can be characterized by “inner” properties ofC and its subobjectsA andB. We also show that the Fitting Lemma and the Krull-Schmidt Theorem hold.
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References
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Günther Richter:Krull-Schmidt for Arbitrary Categories. Contributions to General Algebra, 2 (Klagenfurt, 1982), pp. 319–342, Hölder-Pichler-Tempsky, Vienna, 1983.
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Pareigis, B., Röhrl, H. Complements and the Krull-Schmidt Theorem in arbitrary categories. Appl Categor Struct 3, 11–27 (1995). https://doi.org/10.1007/BF00872947
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DOI: https://doi.org/10.1007/BF00872947