additive and abelian categories
(AB1) pre-abelian category
(AB2) abelian category
(AB5) Grothendieck category
left/right exact functor
(also nonabelian homological algebra)
Context
Basic definitions
Stable homotopy theory notions
Constructions
Lemmas
Homology theories
Theorems
Some authors take pre-additive category to mean $Ab$-enriched category, for example:
Nicolae Popescu, Abelian categories with applications to rings and modules, London Math. Soc. Monographs 3, Academic Press (1973) [MR0340375]
Charles Weibel, An Introduction to Homological Algebra, Cambridge University Press (1994) [doi:10.1017/CBO9781139644136, pdf]
Masaki Kashiwara, Pierre Schapira: Section 8 in: Categories and Sheaves, Grundlehren der Mathematischen Wissenschaften 332, Springer (2006) [doi:10.1007/3-540-27950-4, pdf]
The Stacks Project, 12.3 Preadditive and additive categories [09SE]
Other authors require in addition the existence of a zero object (which, this being the empty coproduct, is the first step towards requiring more general finite coproducts as for an additive category, whence the terminology):
Last revised on August 5, 2023 at 08:00:30. See the history of this page for a list of all contributions to it.