A Quillen Model Structure Approach to Homological Dimensions of Complexes

Abstract

In this paper, we first give an alternative characterization of the derived functor Ext via the Quillen model structure on the category of complexes induced by a given cotorsion pair [Formula: see text] in the category of modules, then based on this, we consider homological dimensions of complexes related to [Formula: see text]. As applications, we extend Gorenstein projective dimension of homologically bounded below complexes (in the sense of Christensen and coauthors) to unbounded complexes whenever R is Gorenstein. Moreover, we extend Stenström's FP-injective dimension from modules to complexes, define FP-projective dimension for complexes, and characterize Noetherian and von Neumann regular rings by these dimensions.