Embedding of categories
HTML articles powered by AMS MathViewer
- by Michael Barr
- Proc. Amer. Math. Soc. 37 (1973), 42-46
- DOI: https://doi.org/10.1090/S0002-9939-1973-0347932-4
- PDF | Request permission
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
- Barr, “Exact categories,” in Exact categories and categories of sheaves, Lecture Notes in Math., no. 236, Springer-Verlag, Berlin and New York, 1971.
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.
- Michel Demazure, Topologies et faisceaux, Schémas en Groupes (Sém. Géométrie Algébrique, Inst. Hautes Études Sci., 1963) Inst. Hautes Études Sci., Paris, 1963, pp. Fasc. 1, Exposé 4, 91 (French). MR 237513
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- 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