We study two kinds of reduction processes of triangulated categories, that is, silting
reduction and Calabi–Yau reduction. It is shown that the silting reduction $\mathcal …

We give a simple sufficient condition for a Verdier quotient ${\cal T}/\{\cal S} $ of a
triangulated category ${\cal T} $ by a thick subcategory ${\cal S} $ to be realized inside of …

We develop the basic properties of $ w $-simple-minded systems in $(-w) $-Calabi-Yau
triangulated categories for $ w\geqslant 1$. We show that the theory of simple-minded …

Let $ A $, $ B $ be two rings and $ T=\left (\begin {smallmatrix} A & M 0 & B\end
{smallmatrix}\right) $ with $ M $ an $ A $-$ B $-bimodule. Given two complete hereditary …

Let $(\mathcal B,\mathbb {E},\mathfrak {s}) $ be an extriangulated category with enough
projectives and enough injectives, and $\mathcal S $ be an extension closed subcategory of …

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 …

Abstract We apply the Auslander–Buchweitz approximation triangles to study (pre) silting
subcategories in a triangulated catego-ry T. An Auslander–Reiten type correspondence …

We define and study a notion of G-dimension for DG-modules over a non-positively graded
commutative noetherian DG-ring $ A $. Some criteria for the finiteness of the G-dimension of …

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 …

Let R be a commutative Noetherian ring and C a semidualizing R-module. We obtain an
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …