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On categories with effective unions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1348)

Abstract

We study an exactness condition that allows us to treat many of the familiar constructions in abelian categories and toposes in parallel. Examples of such constructions include Grothendieck's theorem on the existence of injective cogenerators, the exactness of right exact functors and torsion theories/topologies.

Keywords

  • Full Subcategory
  • Exactness Condition
  • Abelian Category
  • Finite Product
  • Finite Limit

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References

  • B. Banaschewski, Injectivity and essential extensions in equational classes of algebras. Proc. Conf. on Universal Algebra, (1969). Queen's Series Pure Applied Math., 25 (1970).

    Google Scholar 

  • M. Barr, Exact categories. In Exact Categories and Categories of Sheaves, Springer Lecture Notes in Mathematics 236 (1971), 1–120.

    Google Scholar 

  • M. Barr, Non-abelian torsion theories. Canad. J. Math., 25 (1973), 1224–1237.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • M. Barr, Representations of categories. J. Pure and Applied Algebra, 41 (1986), 113–137.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • F. Borceux & B. Veit, On the left exactness of orthogonal reflections. Unpublished manuscript.

    Google Scholar 

  • D. Buchsbaum, Exact categories Appendix to H. Cartan & S. Eilenberg, Homological Algebra, Princeton University Press, Princeton, N.J., 1956.

    MATH  Google Scholar 

  • A. Grothendieck, Sur quelques points d'algèbre homologique. Tohôku Math. Journal 2 (1957), 199–221.

    MathSciNet  MATH  Google Scholar 

  • P. M. Johnstone, Topos Theory. Cambridge University Press, 1977.

    Google Scholar 

  • S. Mac Lane, Duality for groups. Bull. Amer. Math. Soc. 56 (1950), 485–516.

    CrossRef  MathSciNet  Google Scholar 

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© 1988 Springer-Verlag

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Barr, M. (1988). On categories with effective unions. In: Borceux, F. (eds) Categorical Algebra and its Applications. Lecture Notes in Mathematics, vol 1348. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081346

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  • DOI: https://doi.org/10.1007/BFb0081346

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50362-0

  • Online ISBN: 978-3-540-45985-9

  • eBook Packages: Springer Book Archive