We introduce a relativized notion of (semi) normalcy for categories that come equipped with
a proper stable factorization system, and we use radicals (in the sense of module theory) …

We introduce and describe the 2-category Grt♭ of Grothendieck categories and flat
morphisms between them. First, we show that the tensor product of locally presentable linear …

The coherent sheaves defined on a separated noetherian scheme X reflect the underlying
geometry, and they play a central role in modern algebraic geometry. Recent results have …

We provide various ways to characterise $\Sigma $-pure-injective objects in a compactly
generated triangulated category. These characterisations mimic analogous well-known …

It is a well established fact that the notions of quasi-abelian categories and tilting torsion
pairs are equivalent. This equivalence fits in a wider picture including tilting pairs of $ t …

[1504.05271] Hearts of cotorsion pairs are functor categories over cohearts Skip to main
content Cornell University We gratefully acknowledge support from the Simons Foundation …

The notion of extriangulated category was introduced by Nakaoka and Palu giving a
simultaneous generalization of exact categories and triangulated categories. Our first aim is …

We extend work of Balmer, associating filtrations of essentially small tensor triangulated
categories to certain dimension functions, to the setting of actions of rigidly-compactly …

In this paper, we present a generalization of Grothendieck pretopologies--suited for
semicartesian categories with equalizers $ C $--leading to a closed monoidal category of …

Given a tensor triangulated category we investigate the geometry of the Balmer spectrum as
a locally ringed space. Specifically we construct functors assigning to every object in the …