Some remarks on Maltsev and Goursat categories

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.

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Carboni, A., Kelly, G.M. & Pedicchio, M.C. Some remarks on Maltsev and Goursat categories. Appl Categor Struct 1, 385–421 (1993). https://doi.org/10.1007/BF00872942

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Key words

  • Category
  • regular
  • exact
  • variety
  • equivalence relation
  • congruence
  • Maltsev
  • Goursat
  • Kan complex

Mathematics Subject Classifications (1991)

  • 18B10
  • 18G30
  • 08B05