Abstract—The purpose of this paper is to investigate how the relative dimension with respect to right approximations behaves on a recollement (A ,B , C) of abelian categories A , B and C. As an application, the relative dimensions with respect to tilting objects of abelian categories involved in a recollement ( A, B, C) are recovered.

Index Terms—Recollement, right approximation, abelian category.

The authors are with College of Applied Sciences, Beijing University of Technology, Pingle Yuan 100, Beijing, 100124, P. R. China (email: xuerongfu.0098@163.com).

Cite: Xuerong Fu, Hailou Yao, "Right Approximations and Recollements," International Journal of Applied Physics and Mathematics vol. 7, no. 3, pp. 173-181, 2017.