Based on Beligiannis's theory in [Beligiannis, A.(2000). Relative homological algebra and
purity in triangulated categories. J. Algebra 227 (1): 268–361], we introduce and study E …

Let $\mathcal B $ be an extriangulated category with enough projectives and enough
injectives. We define a proper $ m $-term subcategory $\mathcal G $ on $\mathcal B …

Given a cartesian closed category $\mathcal {V} $, we introduce an internal category of
elements $\int_\mathcal {C} F $ associated to a $\mathcal {V} $-functor $ F\colon\mathcal …

As shown by Happel, from any Frobenius exact category, we can construct a triangulated
category as a stable category. On the other hand, it was shown by Iyama and Yoshino that if …

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. In this paper, we first …

In this work we introduce the notion of higher $\mathbb {E} $-extension groups for an
extriangulated category $\mathcal {C} $ and study the quotients $\mathcal {X} _ {n+ …

Let $ k $ be a field, and let ${\mathcal {C}} $ be a $ k $-linear, Hom-finite triangulated
category with split idempotents. In this paper, we show that under suitable circumstances …

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EXTERNAL TRIANGULATION OF THE HOMOTOPY CATEGORY OF EXACT QUASI-CATEGORY …

A notion of balanced pairs in an extriangulated category with a negative first extension is
defined in this article. We prove that there exists a bijective correspondence between …

Let $(\mathcal A,\mathcal B,\mathcal C) $ be a recollement of extriangulated categories. In
this paper, we provide bounds on the coresolution dimensions of the subcategories involved …