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

A category \mathcal{A} is called preadditive if each morphism set \mathop{\mathrm{Mor}}\nolimits _\mathcal {A}(x, y) is endowed with the structure of an

5 авг. 2023 г. · 1. Definition Some authors take pre-additive category to mean Ab Ab -enriched category, for example: Other authors require in addition the existence of a zero ...

31 янв. 2022 г. · An additive category is a preadditive category C where for each pair of objects X1 and X2 there exists an object X and morphisms πk:X→Xk, ιk: ... Examples of preadditive categories that is not additive In what sense are preadditive categories also enriched ... Prove that any preadditive category can be embedded into an ... Другие результаты с сайта math.stackexchange.com

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

7 апр. 2020 г. · A preadditive category is a monoidally enriched category over the monoidal category of abelian groups Ab.

3 сент. 2022 г. · A preadditive category with one object is a categorification of the notion of a noncommutative ring where we interpret the ring addition as the addition ...

21 июл. 2024 г. · pre-additive category: an Ab Ab -enriched category that has a terminal object or initial object and therefore a zero object; Notice however that ...

We work with FI-modules over a small preadditive category, viewed as a ring with several objects. Our aim is to study torsion theories for FI-modules.

30 июл. 2020 г. · On the other hand, rings may be regarded as a special case of small preadditive categories (i.e., small categories enriched over Abelian groups, ...