In the papers of Nakaoka, he introduced the notion of hearts of (twin) cotorsion pairs on
triangulated categories and showed that they have structures of (semi-) abelian categories …

We study the $ t $-structure induced by an $ n $-tilting module $ T $ in the derived category
$\mathcal {D}(R) $ of a ring $ R $. Our main objective is to determine when the heart of the …

It is shown that the category of enriched functors [C, V] is Grothendieck whenever V is a
closed symmetric monoidal Grothendieck category and C is a category enriched over V …

We develop some basic functorial techniques for the study of the categories of comodules
over corings. In particular, we prove that the induction functor stemming from every …

In this paper, we prove a version of Freyd's generating hypothesis for triangulated
categories: if D is a cocomplete triangulated category and S∈ D is an object whose …

In this paper, we introduce a class of exact structures in terms of finiteness conditions of
modules, which are called n-pure exact structures. We investigate the properties of n-pure …

Let A and B be associative rings with unit, Mod-A and Mod-B categories of unital right A-
modules and unital right B-modules respectively. For an AB-bimodule* UB, we consider two …

It is an old observation of Eckmann-Hilton [21], that the homotopy theory of topological
spaces has an algebraic analogue in the module category of a ring. Inspired by the work of …

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Let R be a commutative Noetherian local ring with residue field k. Let X be a resolving
subcategory of finitely generated R-modules. This paper mainly studies when X contains k …