Homological Dimensions of Extriangulated Categories and Recollements

Let (A, B, C) be a recollement of extriangulated categories. In this paper we introduce the global dimension and extension dimension of extriangulated categories, and give some upper bounds of global dimensions and extension dimensions of the categories involved in (A, B, C), which give a simultaneous generalization of some results in recollements of abelian categories and triangulated categories.