On the recollements of functor categories
J Asadollahi, R Hafezi, R Vahed - Applied Categorical Structures, 2016 - Springer
This paper is devoted to the study of recollements of functor categories in different levels. In
the first part of the paper, we start with a small category 𝒮 S and a maximal object s of 𝒮 S …
the first part of the paper, we start with a small category 𝒮 S and a maximal object s of 𝒮 S …
Idempotent completion of pretriangulated categories
J Liu, L Sun - Czechoslovak Mathematical Journal, 2014 - Springer
A pretriangulated category is an additive category with left and right triangulations such that
these two triangulations are compatible. In this paper, we first show that the idempotent …
these two triangulations are compatible. In this paper, we first show that the idempotent …
Green correspondence and relative projectivity for pairs of adjoint functors between triangulated categories
A Zimmermann - Pacific Journal of Mathematics, 2020 - msp.org
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 …
pairs of adjoint functors between three categories. They produced additive quotients of …
Pre-(n+ 2)-angulated categories
J He, P Zhou, X Zhou - Journal of Algebra, 2023 - Elsevier
In this article, we introduce the notion of a pre-(n+ 2)-angulated category as a higher
dimensional analogue of a pre-triangulated category defined by Beligiannis-Reiten. We first …
dimensional analogue of a pre-triangulated category defined by Beligiannis-Reiten. We first …
Homotopy theory in additive categories with suspensions
ZW Li - Communications in Algebra, 2021 - Taylor & Francis
We develop a homotopy theory in additive categories endowed with additive endofunctors,
analogous to Quillen's model categories theory. As applications, we show that Iyama …
analogous to Quillen's model categories theory. As applications, we show that Iyama …
Continuous cluster categories of type D
We construct continuous Frobenius categories of type $ D $. The stable categories of these
Frobenius categories are cluster categories which contain the standard cluster categories of …
Frobenius categories are cluster categories which contain the standard cluster categories of …
The existence of homotopy resolutions of -complexes
X Yang, J Wang - Homology, Homotopy and Applications, 2015 - intlpress.com
In this paper complexes with $ N $-nilpotent differentials are considered. We proceed by
generalizing a defining property of injective and projective resolutions to define $ dg …
generalizing a defining property of injective and projective resolutions to define $ dg …
The realization of Verdier quotients as triangulated subfactors
ZW Li - arXiv preprint arXiv:1612.08340, 2016 - arxiv.org
arXiv:1612.08340v5 [math.RT] 15 Sep 2017 Page 1 arXiv:1612.08340v5 [math.RT] 15 Sep
2017 THE REALIZATION OF VERDIER QUOTIENTS AS TRIANGULATED SUBFACTOR …
2017 THE REALIZATION OF VERDIER QUOTIENTS AS TRIANGULATED SUBFACTOR …
Abelian quotients of extriangulated categories
J He, P Zhou - Proceedings-Mathematical Sciences, 2019 - Springer
We prove that certain subquotient categories of extriangulated categories are abelian. As a
particular case, if an extriangulated category CC has a cluster-tilting subcategory XX, then …
particular case, if an extriangulated category CC has a cluster-tilting subcategory XX, then …