Grothendieck category
In mathematics, a Grothendieck category (named after Alexander Grothendieck) is an AB5 category with a generator. In other words, it is an abelian category A admitting arbitrary coproducts, for which filtered colimits of exact sequences are exact and which possess a generator, i.e. an object E of A such that Hom(E, –) is a faithful functor from A to the category of sets. A dual concept is a coGrothendieck category.
References
- Grothendieck, A. (1957), "Sur quelques points d’algèbre homologique", Tôhoku Math. J., (2) 9: 119–221, MR0102537 . The nLab article on Grothendieck's paper includes links to page scans and translations.
- Jara, Pascual; Verschoren, Alain; Vidal, Conchi (1995), Localization and sheaves: a relative point of view, Pitman Research Notes in Mathematics Series, 339, Longman, Harlow .
External links