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
A pre-additive category is an Ab-enriched category with a zero object.
Pre-additive categories are part of a sequence of additive and abelian categories.
The term ‘pre-additive category’ is often used for any $Ab$-enriched category, for example in section 8 of Kashiwara–Schapira Categories and Sheaves, in Weibel’s An introduction to homological algebra and Popescu’s Abelian categories with applications to rings and modules.
Last revised on March 7, 2014 at 08:45:03. See the history of this page for a list of all contributions to it.