Abelian Categories
نویسنده
چکیده
Abelian categories are the most general category in which one can develop homological algebra. The idea and the name “abelian category” were first introduced by MacLane [Mac50], but the modern axiomitisation and first substantial applications were given by Grothendieck in his famous Tohoku paper [Gro57]. This paper was motivated by the needs of algebraic geometry, where the category of sheaves over a scheme are a central example of an abelian category. Although the purpose of this note is mainly to fix the background on abelian categories needed in our notes on algebraic geometry, we take some time to give the foundations of category theory in some detail. For a full introduction to the subject see [Bor94], [Sch72], [Mit65], [Ste75].
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