… Abstract We introduce relative preresolving subcategories and precoresolving subcat… and
define homological dimensions and codimensions relative to these subcategories, respectively…

… injective, flat) dimension of any left R-module is at most n. In addition, in several cases, for
a subcategory 𝒞 of 𝒯 , we show that the finitistic 𝒞 -projective and 𝒯 -projective dimensions of …

… In homological theory, homological dimensions are fundamental invariants and every
homological dimension of objects is defined relative to a certain subcategory. For example, …

… resolution dimension with respect to a resolving subcategory in … preresolving subcategories
in an abelian category and defined homological dimensions relative to these subcategories, …

… resolution dimension with respect to a resolving subcategory in … preresolving subcategories
in an abelian category and defined homological dimensions relative to these subcategories. …

… the framework of preresolving subcategories by considering … E, the subcategory A still
inherits a rich homological structure from … Let A be a preresolving subcategory of a (deflation-)exact …

… Our aim in this section is to explore some basic results concerning how the homological …
We recall that a subcategory X of modA is resolving if it is preresolving and is closed under …

… dene a new homological dimension, named E-dimension of modules, relative to an injectively
resolving subcategory E of … [ ] ZY Huang, Homological dimensions relative to preresolving …

… subcategories of a triangulated category. Then we give some criteria for computing homological
dimensions … in T , and let J be an E-preresolving subcategory of T admitting a ξ-proper …

… homological dimensions. First we study the relation between these two kinds of relative
homological dimensions … subcategory on which these dimensions are closely related. Namely, a …