A+ CATEGORY SCIENTIFIC UNIT

Almost split triangles in pre-extriangulated categories

Lingling Tan, Dingguo Wang, Tiwei Zhao Colloquium Mathematicum MSC: Primary 16G70; Secondary 18G25. DOI: 10.4064/cm8781-5-2022 Published online: 22 August 2022

Abstract

We consider the notion of pre-extriangulated categories. We give some characterizations of almost split $\mathfrak s$-triangles in a pre-extriangulated category and provide necessary and sufficient conditions for the existence of such triangles. If $\mathcal E$ is an extension-closed subcategory of a pre-extriangulated category $\mathfrak C$ having almost split $\mathfrak s$-triangles, we obtain necessary and sufficient conditions for $\mathcal E$ to have almost split $\mathfrak s$-triangles using the approximation properties of a certain class of objects.

Authors

  • Lingling TanSchool of Mathematical Sciences
    Qufu Normal University
    Qufu 273165,
    Shandong Province, P.R. China
    e-mail
  • Dingguo WangSchool of Mathematical Sciences
    Qufu Normal University
    Qufu 273165,
    Shandong Province, P.R. China
    e-mail
  • Tiwei ZhaoSchool of Mathematical Sciences
    Qufu Normal University
    Qufu 273165,
    Shandong Province, P.R. China
    e-mail

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