specifically in category theory, a preadditive category is another name for an Ab-category, i.e., a category that is enriched over the category of abelian...

In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts. There are two equivalent...

the category of all vector spaces over the field K). Any ring R {\displaystyle R} can be considered as a one-object preadditive category; the category of...

are preadditive categories with one object. The Yoneda lemma remains true for preadditive categories if we choose as our extension the category of additive...

Grothendieck popularized it under the name "abelian category". A category is abelian if it is preadditive and it has a zero object, it has all binary biproducts...

the category of rings cannot be a preadditive category. (However, every ring—considered as a category with a single object—is a preadditive category). The...

opposite category, and vice versa. As mentioned above, a kernel is a type of binary equaliser, or difference kernel. Conversely, in a preadditive category, every...

a preadditive category R with a single object. With this understanding, a left R-module is just a covariant additive functor from R to the category Ab...

category with zero objects, is both a product and a coproduct. In a preadditive category the notions of product and coproduct coincide for finite collections...

more detail, this means that a category C is pre-abelian if: C is preadditive, that is enriched over the monoidal category of abelian groups (equivalently...