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Applied Categorical Structures

, Volume 1, Issue 4, pp 385–421 | Cite as

Some remarks on Maltsev and Goursat categories

  • A. Carboni
  • G. M. Kelly
  • M. C. Pedicchio
Article

Abstract

Our aim is to analyze and to publicize two interesting properties — well known in universal algebra for varieties — that a regular category, and in particular an exact category, may possess: theMaltsev property, asserting the permutabilitySR=RS of equivalence relations on any object, and the weakerGoursat property, asserting only thatSRS=RSR. We investigate these properties, give various equivalent forms of them, and develop some of their useful consequences.

Key words

Category regular exact variety equivalence relation congruence Maltsev Goursat Kan complex 

Mathematics Subject Classifications (1991)

18B10 18G30 08B05 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • A. Carboni
    • 1
  • G. M. Kelly
    • 2
  • M. C. Pedicchio
    • 3
  1. 1.Dipartimento di MatematicaMilanoItaly
  2. 2.School of Mathematics and Statistics F07University of SydneyAustralia
  3. 3.Dipartimento di MatematicaUniversità di TriesteTriesteItaly

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