Proper classes and Gorensteinness in extriangulated categories (Q2300475)

The notion of an extriangulated category [\textit{H. Nakaoka} and \textit{Y. Palu}, Cah. Topol. Géom. Différ. Catég. 60, No. 2, 117--193 (2019; Zbl 1451.18021)] unifies an exact category in the sense of Quillen and a triangulated category in the sense of Verdier-Puppe. In relative homological algebra, the notion of a proper class in an abelian category is standard. The triangulated analogue is due to [\textit{A. Beligiannis}, J. Algebra 227, No. 1, 268--361 (2000; Zbl 0964.18008)]. The paper under review introduces the new notion of a proper class in an extriangulated category. It is used in constructing new extriangulated categories. The Gorenstein projective objects with respect to the proper class are studied, including the Gorenstein homological dimensions. The authors obtain an admissible model structure in the extriangulated category, generalizing a result in [\textit{X. Yang}, Glasg. Math. J. 57, No. 2, 263--284 (2015; Zbl 1316.18015)].