We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type FP n and studying their closure properties with respect to short exact …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

In an arbitrary Grothendieck category, we find necessary and sufficient conditions for the
class of FP n-injective objects to be a torsion class. By doing so, we propose a notion of n …

In the general setting of Grothendieck categories with enough projectives, we prove
theorems that make possible to restrict the study of the problem of the existence of F-covers …

Let k be a field. We show that locally presentable, k-linear categories CC dualizable in the
sense that the identity functor can be recovered as ∐ _i x_i ⊗ f_i∐ ixi⊗ fi for objects x_i ∈ C …

ABSTRACT A natural generalization of locally noetherian and locally coherent categories
leads us to define locally type FP∞ categories. They include not just all categories of …

We define and study opfibrations of V-enriched categories when V is an extensive monoidal
category whose unit is terminal and connected. This includes sets, simplicial sets …

We prove general results about completeness of cotorsion theories and existence of covers
and envelopes in locally presentable abelian categories, extending the well-established …

Let G be a locally coherent Grothendieck category. We show that, under particular
conditions, if a t-structure τ in the unbounded derived category D (G) restricts to the bounded …

Recently a notion of support and a construction of local cohomology functors for [TR5]
compactly generated triangulated categories were introduced and studied by Benson …