Balanced pairs appear naturally in the realm of relative homological algebra associated with
the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural …

In this notes we start with the basic definitions of derived categories, derived functors, tilting
complexes and stable equivalences of Morita type. Our aim is to show via several examples …

We present the concept of cotorsion pairs cut along subcategories of an abelian category.
This provides a generalization of complete cotorsion pairs, and represents a general …

In finitely cocomplete homological categories, co-smash products give rise to (possibly
higher-order) commutators of subobjects. We use binary and ternary co-smash products and …

In a triangulated symmetric monoidal closed category, there are natural dualities induced by
the internal Hom. Given a monoidal functor f^* between two such catgories and adjoint …

Full article: Equivalence of Hearts of Twin Cotorsion Pairs on Triangulated Categories Skip
to Main Content Taylor and Francis Online homepage Taylor and Francis Online homepage …

We survey the basics of homological algebra in exact categories in the sense of Quillen. All
diagram lemmas are proved directly from the axioms, notably the five lemma, the 3× 3 …

We show that the category of mixed Hodge complexes admits a Cartan-Eilenberg structure,
a notion introduced by Guillén-Navarro-Pascual-Roig leading to a good calculation of the …

Let R! A be a homomorphism of associative rings, and let. F; C/be a hereditary complete
cotorsion pair in R-Mod. Let. FA; CA/be the cotorsion pair in A-Mod in which FA is the class …

We study the category Rep (Q, C) of representations of a quiver Q with values in an abelian
category C. For this purpose we introduce the mesh and the cone-shape cardinal numbers …