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Exact colimits and fixed points. (English) Zbl 0358.18016
Small categories \(C\) are characterized such that colimits of \(C\)-indexed diagrams of abelian groups commute with finite limits (i.e. such that colim: \(Ab^c \to Ab\) is an exact functor). This result has been announced by the authors in Bull. Amer. math. Soc. 79, 994–996 (1973; Zbl 0253.18014). The connection to the paper of J. Adámek and J. Reiterman [Trans. Amer. math. Soc. 211, 239–247 (1975; Zbl 0318.18004)] is investigated. In that paper categories \(C\) are characterized with each indecomposable \(C\)-indexed diagram of sets having the fixed-point property. The two results are closely related; in the reviewed paper some results of Adamek and Reiterman are newly proved.

MSC:
18G99 Homological algebra in category theory, derived categories and functors
18F05 Local categories and functors
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