Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories

Abstract: In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. Applications are given to Morita context rings, trivial extension rings, tensor rings and arrow removals. In particular, we provide a new characterization of the upper bound for the Rouquier dimension of finite-dimensional algebras.