39 citations · 109 across the 13 of their papers we have counts for
13 papers
Tensor extriangulated categories
Raphael Bennett-Tennenhaus, Isambard Goodbody, Janina C. Letz +1
A tensor extriangulated category is an extriangulated category with a symmetric monoidal structure that is compatible with the extriangulated structure. To this end we define a not…
The category of extensions and idempotent completion
Raphael Bennett-Tennenhaus, Johanne Haugland, Mads Hustad Sandøy +1
Building on previous work, we study the splitting of idempotents in the category of extensions associated to a pair $(\mathcal{C},\math…
Krull-Remak-Schmidt decompositions in Hom-finite additive categories
Amit Shah
An additive category in which each object has a Krull-Remak-Schmidt decomposition -- that is, a finite direct sum decomposition consisting of objects with local endomorphism rings…
Stratifying systems and Jordan-Hölder extriangulated categories
Thomas Brüstle, Souheila Hassoun, Amit Shah +1
Stratifying systems, which have been defined for module, triangulated and exact categories previously, were developed to produce examples of standardly stratified algebras. A strat…
Idempotent completions of -exangulated categories
Carlo Klapproth, Dixy Msapato, Amit Shah
Suppose is an -exangulated category. We show that the idempotent completion and the weak idempotent completion of are again…
The category of extensions and a characterisation of -exangulated functors
Raphael Bennett-Tennenhaus, Johanne Haugland, Mads Hustad Sandøy +1
Additive categories play a fundamental role in mathematics and related disciplines. Given an additive category equipped with a biadditive functor, one can construct its category of…
The index with respect to a rigid subcategory of a triangulated category
Peter Jørgensen, Amit Shah
Palu defined the index with respect to a cluster tilting object in a suitable triangulated category, in order to better understand the Caldero-Chapoton map that exhibits the connec…
Grothendieck groups of -exangulated categories and a modified Caldero-Chapoton map
Peter Jørgensen, Amit Shah
A strong connection between cluster algebras and representation theory was established by the cluster category. Cluster characters, like the original Caldero-Chapoton (CC) map, are…
Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories
Souheila Hassoun, Amit Shah
It was shown recently that the heart of a twin cotorsion pair ((S,T),(U,V)) on an extriangulated category is semi-abelian. We provide a sufficient condition for the heart to be int…
Examples and non-examples of integral categories and the admissible intersection property
Souheila Hassoun, Amit Shah, Sven-Ake Wegner
Integral categories form a sub-class of pre-abelian categories whose systematic study was initiated by Rump in 2001. In the first part of this article we determine whether several…
Transport of structure in higher homological algebra
Raphael Bennett-Tennenhaus, Amit Shah
We fill a gap in the literature regarding `transport of structure' for (n+2)-angulated, n-exact, n-abelian and n-exangulated categories appearing in (classical and higher) homologi…
Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories
Amit Shah
We generalise some of the theory developed for abelian categories in papers of Auslander and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some Au…
Quasi-abelian hearts of twin cotorsion pairs on triangulated categories
Amit Shah
We prove that, under a mild assumption, the heart H of a twin cotorsion pair ((S,T),(U,V)) on a triangulated category C is a quasi-abelian category. If C is also Krull-Schmidt and…