Let A be an abelian category. A subcategory X of A is called a resolving subcategory if X is closed under extensions and kernels of epimorphisms and contains all projective objects of A. In this paper, we consider the X -resolution dimensions and special X -precovers for a resolving subcategory X of A. Many results in Araya et al. (J Math Kyoto Univ 45:287-306, 2005), Auslander and Bridger (Mem Am Math Soc(94), 1969), Avramov and Martsinkovsky (Proc Lond Math Soc 85:393-440, 2002), Christensen (2000), Christensen et al. (J Algebra 302:231-279, 2006), Holm (J Pure Appl Algebra 189:167-193, 2004), Holm and J?rgensen (J Pure Appl Algebra 205:423-445, 2006), Sather-Wagstaff et al. (Algebr Represent Theor 14:403-428, 2011), Takahashi and White (Math Scand 106:5-22, 2010), White (J Commut Algebra 2:111-137, 2010) and Xu (1996) are generalized.
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