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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Embedding of categories


Author: Michael Barr
Journal: Proc. Amer. Math. Soc. 37 (1973), 42-46
MSC: Primary 18B15
DOI: https://doi.org/10.1090/S0002-9939-1973-0347932-4
MathSciNet review: 0347932
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Abstract: In this paper we generalize the notion of exact functor to an arbitrary category and show that every small category has a full embedding into a category of all set-valued functors on some small category. The notion of exact is such that this result generalizes the author's exact embedding of regular categories and, indeed, Mitchell's embedding of abelian categories. An example is given of the type of diagram-chasing argument that can be given with this embedding.


References [Enhancements On Off] (What's this?)

  • [M] Barr, ``Exact categories,'' in Exact categories and categories of sheaves, Lecture Notes in Math., no. 236, Springer-Verlag, Berlin and New York, 1971.
  • [A] Grothendieck, Techniques de construction en géométrie analytique, Séminaire Henri Cartan, 1960/61, fasc. 1, Exposé 11, École Normale Supérieure, Secrétariat mathématique, Paris, 1962. MR 26 #3562.
  • [M] Michel Demazure, Topologies et faisceaux, Schémas en Groupes (Sém. Géométrie Algébrique, Inst. Hautes Études Sci., 1963) Inst. Hautes Études Sci., Paris, 1963, pp. 91 (French). MR 0237513

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0347932-4
Keywords: Exact embedding, universal regular epimorphism, sheaves
Article copyright: © Copyright 1973 American Mathematical Society

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