Let T be a right exact functor from an abelian category ℬ into another abelian category . Then there exists a functor p from the product category to the comma category (). In this paper, we study the property of the extension closure of some classes of objects in (), the exactness of the functor p and the detailed description of orthogonal classes of a given class in (). Moreover, we characterize when special precovering classes in abelian categories and ℬ can induce special precovering classes in (). As an application, we prove that under suitable cases, the class of Gorenstein projective left Λ-modules over a triangular matrix ring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm{\Lambda }} = \left( {\matrix{ R & M \cr 0 & S \cr } } \right)$$\end{document} is special precovering if and only if both the classes of Gorenstein projective left R-modules and left S-modules are special precovering. Consequently, we produce a large variety of examples of rings such that the class of Gorenstein projective modules is special precovering over them.