Extriangulated categories were introduced by Nakaoka and Palu by extracting the
similarities between exact categories and triangulated categories. A notion of mutation of …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …

Extriangulated categories were introduced by Nakaoka and Palu to give a unification of
properties in exact categories and triangulated categories. We consider in this article the …

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. A notion of proper class in an …

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …

A k-linear triangulated category A is called locally finite provided∑ X∈ indAdimkHomA (X,
Y)<∞ for any indecomposable object Y in A. It has Auslander–Reiten triangles. In this paper …

We exhibit examples of triangulated categories which are neither the stable category of a
Frobenius category nor a full triangulated subcategory of the homotopy category of a stable …

We prove that some subquotient categories of exact categories are abelian. This
generalizes a result by Koenig–Zhu in the case of (algebraic) triangulated categories. As a …

Triangulated categories were introduced in the mid 1960's by JL Verdier in his thesis,
reprinted in [15]. Axioms similar to Verdier's were independently also suggested in [2] …