  We introduce relative preresolving subcategories and precoresolving
subcategories of an abelian category and define homological dimensions and
codimensions relative to these subcategories respectively. We study the
properties of these homological dimensions and codimensions and unify some
important properties possessed by some known homological dimensions. Then we
apply the obtained properties to special subcategories and in particular to
module categories. Finally we propose some open questions and conjectures,
which are closely related to the generalized Nakayama conjecture and the strong
Nakayama conjecture.
