Homology, Homotopy and Applications

Volume 3 (2001)

Number 3

Exact completion and representation in Abelian categories

Pages: 453 – 466

DOI: http://dx.doi.org/10.4310/HHA.2001.v3.n3.a1

Authors

J. Rosický (Department of Mathematics, Masaryk University, Brno, Czech Republic)

E. M. Vitale (Département de Mathématique, Université catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

When the exact completion of a category with weak finite limits is a Mal’cev category, it is possible to combine the universal property of the exact completion and the universal property of the coequalizer completion. We use this fact to explain Freyd’s representation theorems in abelian and Frobenius categories.

Keywords

completions, Mal’cev categories, abelian categories, Frobenius categories

2010 Mathematics Subject Classification

18A35, 18B15, 18E10, 18G05

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