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Metatheorems

  • Francis Borceux
  • Dominique Bourn
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 566)

Abstract

It is common practice, in category theory, to prove metatheorems attesting that if a statement of some given kind holds in a prescribed reference category, the statement holds more generally in a wide collection of abstract categories satisfying a given set of axioms. The cases of abelian categories, with the category of modules on a ring as reference, and the toposes, with the category of sets as reference, are the most celebrated examples to this respect. This preliminary chapter introduces — or recalls — two rather elementary such metatheorems which, in this book, will frequently provide the quickest way to prove results.

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Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Francis Borceux
    • 1
  • Dominique Bourn
    • 2
  1. 1.Université de LouvainLouvain-la-NeuveBelgium
  2. 2.Université du LittoralCalaisFrance

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