An additive functor F: A → B between additive categories is said to be objective, provided
any morphism f in A with F (f)= 0 factors through an object K with F (K)= 0. We concentrate on …

We study determinant functors which are defined on a triangulated category and take values
in a Picard category. The two main results are the existence of a universal determinant …

We study determinant functors which are defined on a triangulated category and take values
in a Picard category. The two main results are the existence of a universal determinant …

We extend Deligne's notion of determinant functor to tensor triangulated categories.
Specifically, to account for the multiexact structure of the tensor, we define a determinant …

To any additive category, we associate in a functorial way two additive categories A (), B ().
The category A (), resp. B (), is the reflection of in the category of additive categories with …

We initiate the study of derived functors in the setting of extriangulated categories. By using
coends, we adapt Yoneda's theory of higher extensions to this framework. We show that …

Auslander and Kleiner proved in 1994 an abstract version of Green correspondence for
pairs of adjoint functors between three categories. They produced additive quotients of …

Let XX be a contravariantly finite resolving subcategory of mod-\varLambda mod-Λ, the
category of finitely generated right\varLambda Λ-modules. We associate to XX the …

The concept of a morphism determined by an object provides a method to construct or
classify morphisms in a fixed category. We show that this works particularly well for …

Let S (n) S (n) be the category of invariant subspaces of nilpotent operators with nilpotency
index at most n n. Such submodule categories have been studied already in 1934 by …