We investigate certain categorical aspects of Voevodsky's triangulated categories motives. For this, various recollements for Grothendieck enriched functors and their derived are established. In order to extend these further with respect Serre's localization, the concept (strict) Voevodsky property Serre localizing subcategories is introduced. This inspired by celebrated theorem on homotopy inv...

We prove that the 2-category of skeletally small abelian categories with exact monoidal structures is anti-equivalent to fp-hom-closed definable additive satisfying an exactness criterion. For a fixed finitely accessible category C products and structure appropriate assumptions, we provide bijections between subcategories C, Serre tensor-ideals Cfp-mod closed subsets Ziegler-type topology. prea...

We prove that the 2-category of skeletally small abelian categories with exact monoidal structures is anti-equivalent to fp-hom-closed definable additive satisfying an exactness criterion. For a fixed finitely accessible category C products and structure appropriate assumptions, we provide bijections between subcategories C, Serre tensor-ideals Cfp-mod closed subsets Ziegler-type topology. prea...

Let $R$ be a commutative Noetherian ring with non-zero identity, $\mathfrak{a}$ an ideal of $R$, $M$ finitely generated $R$--module, and $X$ arbitrary $R$--module. In this paper, for non-negative integers $s, t$ $R$--module $N$, we study the membership $\operatorname{Ext}_{R}^{s}(N, \operatorname{H}^{t}_{\mathfrak{a}}(M, X))$ in Serre subcategories category $R$--modules present some upper bound...

We study degenerations of the Hall algebras exact categories induced by degree functions on set isomorphism classes indecomposable objects. prove that each such degeneration algebra H(E) an category E is a smaller structure E′<E same additive A. When admissible in sense Enomoto, for any satisfying suitable finiteness conditions, we H(E′) this kind. In additively finite case, all form simplicial...