On exact dg categories
X Chen - arXiv preprint arXiv:2306.08231, 2023 - arxiv.org
We introduce the notion of an exact dg category, which is a simultaneous generalization of
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …
the notions of exact category in the sense of Quillen and of pretriangulated dg category in …
Hereditary extriangulated categories: silting objects, mutation, negative extensions
M Gorsky, H Nakaoka, Y Palu - arXiv preprint arXiv:2303.07134, 2023 - arxiv.org
In this article, we initiate the study of hereditary extriangulated categories. Many important
categories arising in representation theory in connection with various theories of mutation …
categories arising in representation theory in connection with various theories of mutation …
The category of extensions and a characterisation of n-exangulated functors
R Bennett-Tennenhaus, J Haugland, MH Sandøy… - Mathematische …, 2023 - Springer
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 …
an additive category equipped with a biadditive functor, one can construct its category of …
Extriangulated ideal quotients, with applications to cluster theory and gentle algebras
X Fang, M Gorsky, Y Palu, PG Plamondon… - arXiv preprint arXiv …, 2023 - arxiv.org
We extend results of Br\" ustle-Yang on ideal quotients of 2-term subcategories of perfect
derived categories of non-positive dg algebras to a relative setting. We find a new …
derived categories of non-positive dg algebras to a relative setting. We find a new …
Stratifying systems and Jordan-H\"{o} lder extriangulated categories
Stratifying systems, which have been defined for module, triangulated and exact categories
previously, were developed to produce examples of standardly stratified algebras. A …
previously, were developed to produce examples of standardly stratified algebras. A …
A resolution theorem for extriangulated categories with applications to the index
Y Ogawa, A Shah - arXiv preprint arXiv:2311.10576, 2023 - arxiv.org
Quillen's Resolution Theorem in algebraic $ K $-theory provides a powerful computational
tool for calculating $ K $-groups of exact categories. At the level of $ K_0 $, this result goes …
tool for calculating $ K $-groups of exact categories. At the level of $ K_0 $, this result goes …
Localization of triangulated categories with respect to extension-closed subcategories
Y Ogawa - arXiv preprint arXiv:2205.12116, 2022 - arxiv.org
The aim of this paper is to develop a framework for localization theory of triangulated
categories $\mathcal {C} $, that is, from a given extension-closed subcategory $\mathcal {N} …
categories $\mathcal {C} $, that is, from a given extension-closed subcategory $\mathcal {N} …
[HTML][HTML] Grothendieck groups of d-exangulated categories and a modified Caldero-Chapoton map
P Jørgensen, A Shah - Journal of Pure and Applied Algebra, 2024 - Elsevier
A strong connection between cluster algebras and representation theory was established by
the cluster category. Cluster characters, like the original Caldero-Chapoton map, are maps …
the cluster category. Cluster characters, like the original Caldero-Chapoton map, are maps …
The index with respect to a contravariantly finite subcategory
The index in triangulated categories plays a key role in the categorification of cluster
algebras; specifically, it categorifies the notion of $ g $-vectors. For an object $ C $ in a …
algebras; specifically, it categorifies the notion of $ g $-vectors. For an object $ C $ in a …