A brief review of abelian categorifications.
A Continuity Criterion for Functors.
A Flatness Criterion in Grothendieck Categories.
A Note on the Structure of Injective Diagrams.
Atomical Grothendieck categories.
Categorical methods in graded ring theory.
Let G be a group, R a G-graded ring and X a right G-set. We study functors between categories of modules graded by G-sets, continuing the work of [M]. As an application we obtain generalizations of Cohen-Montgomery Duality Theorems by categorical methods. Then we study when some functors introduced in [M] (which generalize some functors ocurring in [D1], [D2] and [NRV]) are separable. Finally we obtain an application to the study of the weak dimension of a group graded ring.
Compact topologies on locally presentable categories
Décompositions primaires dans les catégories de Grothendieck commutatives. II.
Décompositions primaires dans les catégories de Grothendieck commutatives. I.
Des propriétés de finitude des foncteurs polynomiaux
We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors (notion introduced by Djament and Vespa) from a small symmetric monoidal category whose unit is an initial object to an abelian category. We prove in particular that the category of polynomial functors from the category of free abelian groups ℤⁿ with split monomorphisms to abelian groups is "almost" locally noetherian. We also give an...
Finite presentation and purity in categories σ[M]
For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcategory of Mod-R containing M. If σ[M] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R is investigated, and the connection between the resulting Ziegler spectra is discussed. An example is given of an M such that σ[M] does not contain any non-zero finitely presented...
Finitely presentable morphisms in exact sequences.
Flache und halbinjektive Funktoren.
Gabriel filters in Grothendieck categories.
In [1] it is proved that one must take care trying to copy results from the case of modules to an arbitrary Grothendieck category in order to describe a hereditary torsion theory in terms of filters of a generator. By the other side, we usually have for a Grothendick category an infinite family of generators {Gi; i ∈ I} and, although each Gi has good properties the generator G = ⊕i ∈ I Gi is not easy to handle (for instance in categories like graded modules). In this paper the authors obtain a bijective...
Localizations of Maltsev varieties.
Morita duality for Grothendieck categories.
We survey some recent results on the theory of Morita duality for Grothendieck categories, comparing two different versions of this concept, and giving applications to QF-3 and Qf-3' rings.
On pure global dimension of locally finitely presented Grothendieck categories
On pure semi-simple Grothendieck categories I
On pure semi-simple Grothendieck categories II
On rings whose flat modules form a Grothendieck category