In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category: ...

29 авг. 2023 г. · Ab denotes the category of abelian groups: it has abelian groups as objects and group homomorphisms between these as morphisms.

In mathematics, specifically in category theory, a preadditive category is another name for an Ab-category, ie, a category that is enriched over the category ...

19 июл. 2024 г. · An Ab Ab -enriched category (or, if small, ringoid) is a category enriched over the monoidal category Ab of abelian groups with its usual tensor ...

In category theory, 'ab' often refers to the category of abelian groups, which are groups that are also abelian under addition.

4 мар. 2018 г. · How to show that Ab(Category of Abelian Groups) is an abelian category? · 1. (2) comes from existence of direct sums, and of kernels/cokernels. I've read that abelian categories can naturally be enriched in In what sense are preadditive categories also enriched ... Definition of a Functor of Abelian Categories Category of abelian groups is not equivalent to its opposite Другие результаты с сайта math.stackexchange.com

18 янв. 2020 г. · Abelian categories are a class of categories that share some of the well known proper- ties of the category of abelian groups Ab, ...

Definition 4: A category is called pre-additive or Ab-category if every hom-set C(a, b) is an additive abelian group and composition is bilinear in a way that ...

An Ab-category is additive when its underlying category has a terminal object and finite products; By the yoga above, this implies that the terminal object is ...

We say \mathcal{A} is a Grothendieck abelian category if it has AB5 and a generator.