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Flat functors and free exact categories

Part of: Algebraic logic Abelian categories Special categories Homological algebra

Published online by Cambridge University Press:  09 April 2009

Hongde Hu
Hongde Hu
Affiliation:
Départment de MathématiquesUniversité du Québec à MontréalMontréal, QCCanadaH3C 3P8 e-mail: hu@math.uqam.ca
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Abstract

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Let C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C. Magno's result on the free exact completion of a small category with finite limits.

MSC classification

Secondary: 03G30: Categorical logic, topoi 18B25: Topoi 18E10: Exact categories, abelian categories 18G05: Projectives and injectives
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 2 , April 1996 , pp. 143 - 156
Copyright
Copyright © Australian Mathematical Society 1996

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