Almost split triangles in pre-extriangulated categories
Volume 171 / 2023
Colloquium Mathematicum 171 (2023), 189-209
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.
