19 окт. 2017 г. · When \mathcal{A} is Hom-finite over a field k, the existence of a generator is the same as the existence of a projective generator, and in case ...

3 дек. 2018 г. · Suppose there is an epimorphism p:GI→X and suppose f:X→Y is a morphism which becomes 0 after applying the functor Hom(G,−). In an abelian category, an object $G$ is a generator iff for any ... Projective objects in abelian categories having non-trivial ... Другие результаты с сайта math.stackexchange.com

Let A be an abelian category. We prove that if A admits a generator M with End A ( M ) right artinian, then A admits a projective generator.

When $\mathcal{A}$ is Hom-finite over a field $k$, the existence of a generator is the same as the existence of a projective generator, and in case there is ...

5 июн. 2020 г. · For this reason, the assumption that an Abelian category has a projective generator plays an important role in homological algebra.

24 нояб. 2020 г. · in a cocomplete abelian category, "compact projective," using either Lurie-compactness or Murfet-compactness, is equivalent to the condition ... In a category with a projective generator, do morphisms from ... Existence of projective generators for a module category Другие результаты с сайта mathoverflow.net

6 июн. 2024 г. · Theorem 3.6. Let C be an abelian category. If C has all small coproducts and has a compact projective generator, then C ≃ R Mod C \simeq R Mod ...

10 апр. 2008 г. · An abelian category is a category where the set of morphisms between any two objects, Hom(A,B), is an abelian group; with some additional properties.

24 нояб. 2010 г. · A tilting object in a abelian category is a natural generalization of a small projective generator. Moreover, any abelian category with a ...

17 мая 2015 г. · We proved a theorem due to Gabriel characterizing categories of modules as cocomplete abelian categories with a compact projective generator.