• Corpus ID: 245123723

The (ET4) axiom for Extriangulated Categories

  title={The (ET4) axiom for Extriangulated Categories},
  author={Xiaoxue Kong and Zengqiang Lin and Minxiong Wang},
Extriangulated categories were introduced by Nakaoka and Palu, which is a simultaneous generalization of exact categories and triangulated categories. The axiom (ET4) for extriangulated categories is an analogue of the octahedron axiom (TR4) for triangulated categories. In this paper, we introduce homotopy cartesian squares in pre-extriangulated categories to investigate the axiom (ET4). We provide several equivalent statements of the axiom (ET4) and find out conditions under which the axiom is… 

Two results of $n$-exangulated categories

n -exangulated categories were introduced by Herschend-Liu-Nakaoka which are a simul-taneous generalization of n -exact categories and ( n + 2)-angulated categories. This paper consists of two



Hearts of twin cotorsion pairs on extriangulated categories

Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories

We give a simultaneous generalization of exact categories and triangulated categories, which is suitable for considering cotorsion pairs, and which we call extriangulated categories.

Triangulated quotient categories revisited

Derived categories, resolutions, and Brown representability

These notes are based on a series of five lectures given during the summer school ``Interactions between Homotopy Theory and Algebra'' held at the University of Chicago in 2004.

Triangulated Categories

For a self-orthogonal module T , the relation between the quotient triangulated category Db(A)/K b(addT ) and the stable category of the Frobenius category of T -Cohen-Macaulay modules is

Neeman , Triangulated Categories

  • 2001